4chan surprisingly is not a free speech platform, nor did it ever pretend to be.

It has fairly bog-standard rules about not being a hateful jerk, it's just that enforcement of those rules is pretty spotty so the sites users consist mostly of hateful jerks.

For a more specific example; 4chan remains the only site to actually ban discussion of gamergate (and then discussion of the subsequent user blowback towards moot) due to it being a harassment campaign.

Was the ban specifically around criticism of moot or gamergate in general?

4chan bans are notoriously ineffective. Since you don't have an account or identity worth banning, most bans are up blocks which are pretty easy to circumvent undetected.

That's why I said try. They could ban IPs or at the very least block tripcodes. I'm not aware of them trying to do so in response to criticism of moot or other owners.

There's screenshots floating around of people's bans for completely arbitrary reasons. Don't know if they're legit.

Probably, though I couldn't point to any particular instance. People definitely catch short "off-topic" bans for shit-talking the jannies though.

Most of 4chan is moderated, but poorly, inconsistently, and capriciously. Each board has its own set of rules, which are sometimes enforced and sometimes not, with different enforcement rates on different boards. Also there are global rules which are generally not enforced, except when they are.