There are plenty of good examples in these videos of women being used as simple objects, like trophies, as a prize for the male protagonist to win, with no will or agency of their own. And there are some pretty embarrassing examples of blatant sexism in video game advertising, such as the Legend of Zelda: Ocarina of Time television ad from 1998 that contains the splash text, "And in the end, willst thou get the girl? Or play like one?"
I wouldn't argue for a second that Sarkeesian doesn't have a lot of good points or that the games industry has been a shining example of gender equality and female empowerment. However, I do have a strong suspicion that she is seeing games a little too strongly through a feminist lens and is not stepping back to consider other possible explanations for some of the things that she insists must be sexism and mysogyny at their core.
It is a common problem with people who are passionate about a particular cause to have a tendency to see everything through the lens of that cause. So you get feminists who interpret everything men do through a lens of sexism, racial minorities who interpret the actions of other races as racially motivated, or anti-religious people like myself tending to interpret the actions of religious people as always being religiously based. Being well aware of this flaw in myself and constantly looking out for when I'm overreaching, I also try to notice when other people do it, and point it out, even when I'm in general agreement with them, as is the case here with Sarkeesian.
I think the fundamental issue here is that she is falling foul of a version of: "Don't attribute to malice what you can attribute to incompetence". Though in this case I think it's: "Don't attribute to malice what you can attribute to expedience".
Games, like movies and television, often have the need to set up characters and situations quickly, so they can get on with their main purpose. As a result, we often see characters that fit well worn stereotypes, and clichéd situations and character motivations. This is done so that the audience will be able to relate to the situation and get on board the narrative. In a medium such as novels, this is less necessary since there is more time to develop characters and circumstances, but when you're trying to quickly get things established and get the audience on board, tropes, clichés and stereotypes are the standard way to do it.
So, given that we know most games are made with men as the target audience, typically teenagers or young adults, it shouldn't be surprising that games will fall back on tropes that this audience will understand. Like action movies, a lot of games are primarily about the action and not focused on telling a deep story or fleshing out characters in any kind of substantial arc. You need a simple, quick to explain motivator for the main character that justifies his actions throughout the game/movie to follow.
The Protective Instinct
Most men have a hardwired instinct to protect, in the same way most women have a natural nurturing instinct. I'm not going to go into the obvious evolutionary reasons behind this; it should be fairly common knowledge. But men, particularly young men, also have the desire to gain respect, be seen as brave and heroic, and so many of our stories and tropes over the years have been based around this.
And this is where women fit in so perfectly. Having a woman in distress as the primary motivator in a story taps in to both the male's protective instinct, that need to save a woman in danger, and also gain respect and be a hero. Combining all of this together is a powerful motivator that most men understand immediately, which serves perfectly for a lot of games.
You could make a game about the hero trying to get back his stolen car, but it's just not going to resonate in the same way. Even the story about rescuing another man is just not the same. Rescuing a son will resonate a lot more than these previous two, but there's just something about protecting a woman that is different.
Now, this in itself could well be an example of sexism in the sense that men have a tendency to see women as helpless or in need of protection, but it's based on a long evolutionary history of men fighting other men for the possession of women. We may not live in that kind of world so much these days (at least not in Western countries), but the instinct is still there. Removing it would be like telling a woman not to feel warm and fuzzy when she sees a newborn baby. These are some of our deepest instincts, evolved for good reasons.
One other thing to consider is that games often have the protagonist killing hundreds or thousands of people in a way that could only be considered psychotic in the real world. Like movies, they need to be heightened versions of reality to be satisfying, since they are experienced at a distance. We're not actually in the scene, but experiencing it through a screen. So, while in real life, experiencing shooting a single actual human being would be a traumatic experience, in a game or movie, we get to experience a taste of the adrenaline and badassery of being an action hero, without the guilt and trauma of reality.
However, we still need to have a believable motivation for our actions. Especially as games get more realistic, we need to feel like the character isn't going around killing people because his ice cream fell out of the cone. It needs to be reasons that resonate: saving a loved one, avenging a murder, saving the world.
In the end, I definitely feel that we should keep trying to increase the maturity of the games industry, producing games with more complicated characters and narratives, and giving women more to do than be a trophy. We can do this while still acknowledging that sometimes tropes are used simply because they allow a game to get to its primary purpose faster, and not with the intention to be sexist, racist, or any other -ist.
The Last of Us comes out in a few days time, and it's currently being heaped with praise in reviews because of its believable characters. I'm sure this praise is well deserved, and this will be one example of a game that tries to flesh out its female character beyond the usual clichés. But at its heart, it's a game about a middle aged man and a 14 year old girl trying to survive, and if you think they won't be taking advantage of the natural protective instinct of every male who plays this game, you're crazy!