It's not WWIII if 5/6 of humanity remains neutral

Is this post about anything more than semantics? If yes, why does it matter?

I tend to use "world war III" as shorthand for "big nuclear powers committed enough to actually launch their mutually-assured destruction mechanisms".   I assign fairly small probability to this being small enough for any significant portion of the world to escape chaos and destruction.  Even if many survive, there will be so much disruption that "local violence" is common.

Additionally, I think it's likely that big non-Western powers would use the opportunity to perform violence on their neighbors, making it a true world-wide war zone, even if it's not technically the "same" war officially.

It's not a world war if China, India, Indonesia, Pakistan, Brazil, Nigeria, Bangladesh, Mexico, Japan, Ethiopia, the Phillipines, Egypt and Vietnam aren't fighting.

As a nitpick, see the Kuril Islands and Japan recently calling them "ancestral territories"

This seems to be based on your own definition of  World War.  Instead of population, you could have used the GDP of the countries involved, the number of countries or even the total surface. I do agree that a war between Pakistan and India wouldn't be a World War,  which suggests in fact that the definition you are using here does not really capture what a World War is.

I suspect that massive destabilization following the precipitous fall of most of the great powers (NATO + Russia at the least) would result in war on every continent (sans Antarctica). If Asian countries don't get nuked in this scenario like you suppose, I think it's quite plausible general war in Asia would follow shortly as the surviving greatest powers jockey for dominance. If we posit the complete collapse of U.S. power projection in the Pacific, surely China is best positioned to fill the void, and I don't think it's clear where they'd draw the new lines.

The concept of "world war" doesn't need to mean "most of the world's population is involved in this war," not when nuclear weapons are at stake. A nuclear exchange between NATO and Russia is world-shifting in a way that a nuclear exchange between Pakistan and India is not. Calling nuclear war between major Western powers (which will almost certainly have devastating economic and physical effects on the entire world) a "world war" seems perfectly reasonable at that point, even if most of the world is not directly involved.

A point worth considering is the difference between agency of the belligerents vs. the consequences of the war. Even in WWII, the consequences of the war were mostly local for the belligerents; France and Germany, Russia, Japan and China were all much more affected by the destruction of their cities and fields than they were anything that happened with international trade or similar.

The nuclear winter scenario is one that affects all countries similarly, insofar as nuclear winter is the worst thing for the neutrals and also the worst thing for the belligerents, even granting multiple nuclear strikes. Depending on how a person ranks swift incineration vs inevitable starvation, being a belligerent might even be less bad.

I'm not sure how to weight it, but a point worth observing from the WW2 comparison is the absence of colonial possessions and the presence of diplomacy or opportunism to bring additional countries into the war on either side. For example, British India resulted in modern Bangladesh, India, and Pakistan all being involved in the war based on the European theatre of the conflict, as opposed to the much closer and materially-more-relevant China/Japan theatre. An example where the conflict could easily extend is that both Russia and the United States maintain military assets in different host countries. Examples: Syria is host to Russia's assets which operate in the Mediterranean, which is NATO's underbelly; Japan and Korea host American assets which can reach Russian territory.

Regarding China, which is the largest x-factor in terms of both outcome and this criteria: it seems to me that the only thing preventing their involvement through a similar string of diplomatic escalations is the judgment of the Chinese government. Among other things, it becomes hugely in Russia's interest to bring them into the war, in a manner analogous to it being in Britain's interests to bring the US into WWII.

There are too many vectors for a NATO/Russia conflict in Ukraine to extend throughout the rest of Asia at least for me view this is as just a European war by default.

Does cyberwar count? Including social manipulation on social media on a global scale?

Hey uhhhhhh is there a map of the world showing likely nuclear war targets and expected fallout radius? Like Nukemap. Asking for, uhhhh, a friend in a maybe-risky area.