The point of a game is not to win, and you shouldn't even pretend that it is

90% of games are designed to be fun. Meaning the point is to stimulate your brain to produce feel-good chemicals. No greater meaning, or secret goal. To do this, they have goals, rules, and other features, but the core loop is very simple:

1. I want to get a dopamine hit, therefore
2. I open up a game, and
3. The game provides a structure that I follow, subordinating my "real life" to the artificial goals and laws of the game
4. Profit!

Okay, I'm not opposed to the project of inventing fun games with no one winner - I mean, I enjoy Dungeons & Dragons - but I think games with one winner are awesome. I like the discipline imposed by them.

I'm not sure I can put into words what I mean by discipline; it's related to the nameless virtue. But, for example, sometimes in a computer game I find myself thinking, "wow this game is badly designed; it'd be more fun and realistic if it rewarded a good balance of archers and spearmen and cavalry, but I'm pretty sure the archer unit is so cheap and high ground is so accessible that I can just spam the archer unit and win". I then have a choice; I can do the thing that seems fun and elegant to me and build a realistic army, or I can spam the archer unit and win. I can either complain, or I can win.

To the extent that I'm stretching a rationalist muscle in games at all - and often I'm not, I'm just having fun, not everything I do needs to be justified as rational and virtuous - I think it's that muscle: "ignore the temptation to adopt a really cool and fun map, and instead use a map that actually describes the territory". This requires a certain harshness; I can do stuff that makes me feel good and lose and keep losing until I change my strategy. I can complain, "The designers clearly intended this thing to be a powerful strategy, so it should work!" - and if it isn't actually the best strategy, I will lose. This teaches me to abandon what "should" be true, and pay attention to what actually is true.

The original designers' intent very rarely comes across in games without very extensive testing and rebalancing IME. Maybe the game is designed so that you need to do X to win, but the very best competitive players will often create a metagame where everyone ignores X and does Y to win. Preventing this from happening requires so much playtesting, and then if your game gets a big enough audience that there's a semipro or pro scene, it generally happens anyway. It's like trying to beat the market; you're just one game designer, and arrayed against you are the forces of thousands of smart people all trying to win your game. Unless you write "you can't win without doing X" into the rulebook, or unless your game is very very simple, someone will find a way to win without doing X. (Maybe this isn't true for board games, but I think it's pretty true about video games, which are more of my experience. Esports games are constantly patched to tune down the dominance of whatever the latest powerful strat is. Card games also often have the problem of a card needing to be changed because, in combination with some other card, it's being used in an unexpectedly powerful way. So I think it's probably applicable to board games that are played competitively.)

I think your project is cool, but I also like games with a winner and a loser; I don't think you need to explain why they're bad to explain why your thing is good!

Does your argument also apply to physical sports? If not, what makes table tennis different from monopoly? 

I think you're missing an important point of games: fun.

I think that's the biggest reason people play games.

All of the things you've mentioned can be fun. And sometimes people play games to understand each other better, or to learn. But they largely do it because those things are fun, too.

We're wired to like fun because it causes us to practice, and to win. But we genuinely like fun.

(winning is usually a lot of fun; the problem is that others have to lose, so less total fun is produced in a one-winner game).

That's mostly why people play games, and you've got to take that into account in your game design.

I have had a similar mindset in games for a long time. This exploration you describe in my experience felt like the fastest way to improve in games (and in maths: when a teacher says that some method would not work to solve a problem, without telling me why, I am likely to try and see myself, how the edge cases invalidate the method). Apart from giving a broader intuition about the subject I believe it enreaches the "toolkit".

There is a 1v4 computer game Dead by daylight. The thing that attracts me is the ability to make your own build - set of powers your character will enter the match with. There are more than 10^12 combinations, and that creates an optimisation problem. Community of the game has agreed on around 12 best builds, and a new player could just take one of them into the game without understanding why they are considered best. But I decided to do exploration and play with random builds. This opened to me a vast space of rare power synergies the community never agrees to discuss. They throw unconventional builds and playstyles into the bin.

If I had friends who play computer games, I would really want to convey an experiment. I would ask them to start learning the game, completing the same amount of matches per weekend. One group would be presented with classical introduction, materials and videos that explain the current meta ("best" builds and methods of winning, as community states), and they would only be limited to the professionals' recommendations. Another group would be allowed to play with only random builds and would not be presented with classical "how to win" materials, instead they'll see videos where gamers explore the space of possible builds, try to win by unconventional methods, experiment with setting weird winning criterias, playing with handicaps, or other things which are considered "inefficient" by the community majority.

My intuition says that the second group would improve at the game much faster and after 50 matches be on a higher level (even though they might have lost more matches during training). They will find the powers that fit them better. They will know more mechanics of the game, that they could apply in edge cases. They might play on a psychological level by surprising opponents with some weird strategy.

One of the reasons I did not start that little experiment is the absence of visible Elo in the game. The only way of testing which group is better currently is a face-to-face matches between them, but that might not be the correct evaluation of skill. Rock-paper-scissors problem: when one group is taught to only throw rock and another is taught to adapt, the outcome is trivial. True testing would need many matches against random opponents to make statistically significant conclusions. I have not yet found people with dedication for that. So, there is a strong belief that I have not found a way to test.

Hobbes: Our poster didn't win?
Calvin: I still can't believe it.
Calvin: What a miscarriage of justice! This contest was a joke! Obviously the judges were biased against us from the start!
Hobbes: Well, the important thing is that we tried our best.
Calvin: The important thing is that we lost!
Hobbes: (rolls eyes) Oops, I forgot that the purpose of competition is to divide people into winners and losers.
Calvin: What's the point of trying if you can't be a winner?

https://www.gocomics.com/calvinandhobbes/1993/05/07

I think this is pointing at something real. Have you looked at any of the research with the MDA Framework used in video game development?

There are lots of reasons a group (or individual) goes to play a game. This framework found the reasons clustering into these 8 categories: 

1. the tactile senses (enjoying the shiny coins, or the clacking of dice)
2. Challenge (the usual "playing to win" but also things like speedrunners)
3. Narratives (playing for the story, the characters and their actions)
4. Fantasy (enjoyment of a make-believe world. Escapism)
5. Fellowship (hanging out with your buds, insider jokes, etc.)
6. Discovery (learning new things about the game, revealing a world and map, metroidvania-style games)
7. Expression (spending 4 hours in the character creation menu)
8. Abnegation (cookie cutter games, games to rest your mind and not think about things)

The categories are not mutually exclusive by any means, and I think this is pointing at the same thing this post is pointing at. Namely, where the emotional investment of the player is. 

None of your other candidates are the point either.  The point that can be named is not the true point.

It's an important observation that most, if not all, human activities have more than one benefit, often at different levels of abstraction and on different timeframes.  "the point" is an ambiguious framing - you should think more like "one point of most boardgames is to win".  Another point is to practice a specific mix of zero-sum and non-zero-sum subgames, to learn about optimization, cooperation, and competition.  Another point is to have fun with people and grow your bonds.  Another point is ...

There is no "real objective", there are only different weights (over time and across participants) put on the many reasons to do something.

I've played a fair bit of 18xx ("train games", but more about stock-manipulation) games with a specific group of friends.  These games contain zero external randomizers, beyond the initial selection of turn ordering (which then changes based on in-game effects).  We played to win, and it would be un-fun if we didn't.  That includes competitive aspects like blocking others' routes and "thushing" their stock.  Optimizing one's outcomes in the absence of smart, motivated, adversaries does not excercise the same learning or enjoyment.

But we certainly did not play because each of us expected to win, and certainly saw good value in the game even when not winning (which sometimes could be known early, and certainly felt like it to all of us, even the winner, at various points in the course of a game).  But the details, strategy, conversation, and experimentation toward winning was the driver for most of the other value.

I've also played a lot of cash and tournament poker, with friends and strangers.  It's hard to claim that winning isn't the primary goal of the game, and my primary motivation for playing in public cardrooms (where I don't know the other players well enough for bonding and shared joy to be the motivator).  But even then, there will be plenty of losing hands, too many losing sessions, and not enough immediate feedback to make "long-term profit" the only element of the game that matters.  It matters on one level - if I lost consistently, I'd make the financial choice to stay away.  On another level, the analytic and "what-if" optimization of individual sub-hand decisions, as they affect both later streets and later hands, are fascinating and fun, regardless of outcome of that hand.

Have you read Playing To Win, by David Sirlin? It makes many of the points that you make here, but it doesn't shy away from winning as the ultimate goal, as you seem to be doing. Sirlin doesn't fall into the trap of lost purposes. He keeps in mind that the goal is to win. Yes, of course, by all means try new strategies and learn the mechanics of the game, but remember that the goal is victory.

This may be a healthy attitude to have as a player but it's a terrible attitude to have as a game designer