I agree overall apart from one point. In the video, Jim said that gamers lash out against these arguments because they "fear that games will be taken away from them". I think that people lash out against accusations of sexism/racism/whatever because its easier than having to admit that you might be a little bit sexist/racist/whatever.
Put it this way. We all like to think of ourselves as educated, rational and generally kind hearted people. We live in the 21st century, we all have a vague idea about what sexism is and that its wrong. We know that buses shouldn't be segregated and that women should be allowed to work and vote. However, just because we understand it intellectually, doesn't mean that it translates into our everyday actions.
Its quite rare that we actually step back and evaluate our everyday behaviours. Let's imagine you watch a movie and chat with your friends about it afterwards. You'll probably talk about the acting, the action scenes, the script. If its a movie with an explicit Big Idea, like the Matrix, you may even talk about that. However, unless you've just watched The Hours, how often do you leave the movie and discussed the portrayal of the female characters?
Each one of us probably commits a number of minor sexist/racist/ageist actions in our everyday lives without really calling them into question. If someone makes a joke about women getting back in the kitchen, they aren't going to stop and think "how does this joke reinforce negative stereotypes?". When someone points out that a movie or a game we enjoyed might be sexist or racist, then we have to face up to the uncomfortable truth that we may be sexist or racist.
This isn't a nice thing for anyone to admit, so instead a lot of people just attack the source. Whenever someone is told they said something inappropriate, its always "it's political correctness gone mad" or "oh, you can't take a joke" rather than "that was ill thought out and offensive, I'm sorry".
I doubt that very few of the people that attacked Sarkeesian would say "yes, I'm sexist, I believe in the subjugation of women".
We've all experienced similar phenomena, when people would rather criticise us when they are clearly in the wrong. People criticise you for working/studying hard because its easier than to admit they aren't working/studying hard enough. Or if you tell someone that you are on a diet, they are likely to say something along the lines of "all that fad diet stuff is mumbo jumbo and snake oil", because they don't want to face up to the fact that they eat badly.