You should not lump /r/kotakuinaction and /r/conspiracy in the same category as /r/fatpeoplehate. They aren't even mildly offensive - the only relationship here is that they tend to be zealous about freedom of speech, and therefore angry about the removal of /r/fatpeoplehate.
I would classify them strongly as "political speech", which /r/fatpeoplehate was not.
/r/conspiracy was harassing a daycare in Utah. I don't like to use that term lightly but yes, actual harassing. As in, the subreddit was obsessed with it because it had some records online that made them think it was secretly running some kind of malicious operation. people were going there and surrepititiously scouting the place and sending back photos and talking to neighbors. Admins were deleting posts, which is why it turned into a "free speech" issue for them and a bunch went to voat.
The difference between those subreddits and the ones banned where:
1) Magnitudes more users -and-
2) Mods were actively promoting harassment of individuals
Reddit admins had to step in because people were being bullied and receiving violent threats, in part due to actions taken by Mods of these large communities built on prejudice and harassment.
They are in the same category as far as SJWs are concerned because the are not "politically correct", or put simply they are not taking a knee and kissing the ring as SJWs demand.
This is why they have no problem simply telling lies about these subreddits (as they are lying about FPH). The entire point of KotakuInAction and GamerGate is to point out how dishonest this movement is... and what is the response? They lie about them!
Expecting dishonest people to respond with anything but more lies is a silly expectation.
The morally repugnant SJW movement is, at its core, a political movement. They succeeded in turning /r/politics into a monoculture around a single thought and the entire purpose of /r/SRS and all their activism on tumblr is to shame and harass anyone who thinks differently into submission.
I would classify them strongly as "political speech", which /r/fatpeoplehate was not.