Maybe you personally don't but the SJ movement you seem to support certainly does that to random social media users and not just mocks them but goes after them and their families and tries to get them fired from their jobs.
This certainly seems rather accusatory, seeing as (as far as I know) Ozy doesn't actually support doxxing random social media users and is certainly not responsible for the actions of the entire SJ movement.
However, your point - that while Ozy is not contributing to this norm, other people are - is worth addressing.
Ozy's claim here, as far as I can tell, is that, even if people on Our Side stopped doing bad things, that wouldn't automatically cause people on The Other Side to stop doing bad things. Do you actually think that Ozy is wrong about this, or do you only disagree that the evidence they present is sufficient?
This may be true but vicous behaviour will encourage political oponents to retaliate in kind. It's called tit-for-tat and this article suggests you don't understand it.
Even if one side stopped doxxing, the other side would probably keep doxxing.
Tit for tat doesn't work very well if everyone just keeps defecting on each other. This is unusually likely to happen - and it is in fact what's happening - because there are hundreds of individual actors who aren't particularly coordinated. If you dox SJ #1 and SJ #1 repents and decides never ever to dox again, SJ #2 doesn't necessarily care.
Also, many people who dox don't conceive of the situation in this way. "I doxxed someone, so in return I got doxxed. Therefore, I will never dox again." No, when they dox people it's good because those people are bad; when they get doxxed it's bad because they're a good person.
In order to resolve the problem where everyone keeps defecting, it takes more than just one side saying, "Oh, I'll cooperate every time!" It takes some kind of unifying authority or agreement or something.