I've watched a couple of Anita's videos, and as I recall, she starts with a disclaimer to the effect that it's possible to enjoy many aspects of something and still recognize that it reflects problematic attitudes. So I don't think she's saying that people shouldn't play any of the games she singles out, just that there are problems in how they portray women. As for the "why is this a big deal" school of thought, another point I'd make (and I'm not sure if Anita herself mentions this or not) is that it's possible for perfectly well-meaning people to reflect prejudiced or stereotypical attitudes without even being aware that they're doing it, and that some of these portrayals can subtly reinforce those attitudes among the audience.
I do remember her pointing out a bunch of games where the story is set in motion by a female family member or love interest of a male protagonist being murdered, kidnapped, or otherwise victimized. At first, one might be tempted to respond, "OK, but the murderer/kidnapper is the villain here and the games never pretend otherwise, so how is it offensive to women? After all, bad things happen to good people and the female characters didn't do anything wrong." On the other hand, maybe this sort of setup does reinforce a more general stereotype of women as helpless and needing men to protect them or get them out of bad situations, even if the game writers and players might not be consciously aware of that.
I think that, ultimately, this post accurately summarizes what she is trying to get across. Which, to be honest, I don't have an issue with at all. There's definitely some truth to her message.
I think that some people rightfully point out that she cherry picks her data, which is fine, but then she doesn't really acknowledge context. This can come across as either disingenuous representation of data or outright dishonesty, depending on how you view her. To be honest, I have often wondered if people's visceral reaction to her message is more about her as a person and less about what she is saying.
All of this being said, the people who have derided her and insulted her and demeaned her and threatened her have only served to push me to be sympathetic towards her. If people simply said, "Meh, I don't like how she puts her message forward." or "I disagree with her and here's why <with evidence>", I'd understand that. But when people call her terrible misogynistic names and say she's a charlatan and a criminal and blah, blah, blah, well, that makes me listen less to their side of the story. And I say that as someone who isn't really a fan of hers to begin with (I'm pretty neutral on her).