I'm not really au fait with it all.
But, from what I can see, it started a with a story about Zoe Quinn shagging a bunch of video game journalists to get coverage for her game (Depression Quest) getting revealed by her ex-boyfriend. Which lead to gamers getting pissed off because they're not carrying any journalistic integrity.
So gamers then said "Fuck you guys, tell the truth", and they said to Zoe Quinn "Fuck you too, you slag".
As for the "sexism" thing, again, from what I've seen outside of one sided arguments, it's not really about that, people seemingly welcome women into the industry with open arms.
However, it turned to sexism when Anita Sarkeesian and Jonathan Mcintosh stuck their collective oar in with "That's sexist, that's sexist, all this is sexist, and you're sexist too!" to which people said "Fuck off, Anita" which then became "Ahhhh, you're harrassing me! These are GamerGaters!" Which the gaming journalists, who were already under attack because of the Zoe Quinn thing then glaumed onto that and said "See, you're sexist, gamers are sexist"
Sarkeesian and McIntosh ran with it, because they could get more money out of it, ran to the press and said "See, GamerGate is harrassing me, I'm just sharing my opinion... an incendiary, poorly researched, out of context, and sometimes even outright lying, usually to provoke them into respoding to me... but still, I'm a Damsel in Distress... no, it's not sexist if I say I am, it's only sexist if YOU say I am!".
Like I said though, I'm not au fait on it, so I'm probably dead wrong.