Before I say anything about this video, I'll reiterate something that Sarkeesian herself says right at the beginning: you can look critically at the problematic elements of something and still enjoy it at the same time. In other words, you can still like Star Fox Adventures (to use an example from the video) even if its portrayal of Crystal is pretty dumb.
Speaking of Star Fox Adventures, the video presents a bit of history I didn't know - that it was originally going to be a standalone game called Dinosaur Planet with Crystal as the hero, but was converted into a Star Fox game with Crystal as a secondary character. That scene where Fox finds her trapped in the crystal is pretty atrocious, even if it was supposed to be cheesy/funny.
Side note, I can't believe that some of those scenes actually made it into games, and that those commercials actually aired on TV. "Willst thou get the girl? Or play like one?" Wooooooowwwwww.
One of the only flaws I see in this video is the argument that imprisoned male characters are able to escape through their own strength or ingenuity. The escape isn't because they're male, it's because they're the playable character. Agency and ability is important to the role and story of the player character regardless of sex/gender. Of course I wouldn't say it's just coincidence that player characters happen to be male most of the time, but it's not the player's maleness that allows them to escape, but rather their status as playable. After all, you don't see games that end with the player being imprisoned in the first hour.
"Double Dragon Neon in 2012 reintroduced gamers to this regressive crap yet again..."
This is the other flaw. It's an out-of-place bit of emotional editorializing in a piece that's otherwise well researched and well presented. I hope future videos leave out the sarcasm as effectively as most of this one did, without little slips like this one line.
There is one... well, not exactly counter-argument or justification, but one piece of information that isn't present in this video. Early video games didn't have the capability or memory space to provide complex or subtle stories, or even very much text. With this in mind, having a ten-second cutscene showing the villain abducting a woman was a simple and convenient shorthand to provide the entire story and motivation for these early games. Lazy? Maybe, but effective and required little of that precious memory space. Having the villain steal an inanimate object would have been less efficient, since you'd have to know what the object is and why the hero cares about it (though it would've worked perfectly in, say, an Indiana Jones game, or something similarly themed). To be fair, though, developers lost this excuse very quickly as games became bigger and more complex. By the time the Super Nintendo rolled around, developers had plenty of resources to create a deeper story - it's just that many chose not to.
I was worried, based on the title of the series - Tropes vs Women in Video Games - would only look at the negative portrayals and ignore the positive (or at least less problematic) representations. This video does acknowledge that Zelda, while still being a damsel in distress most of the time, does have more agency and play a bigger role in the story than does Peach, especially in Ocarina of Time and Wind Waker. And right at the end, Sarkeesian mentions that in part 2 of Damsel in Distress, she'll look at games where the developers have tried to flip the convention.
So overall this video is quite fair and well-researched, so much that I actually learned a couple of things about video game history. When I first heard about the series I did have that instinctive "oh no" reaction that probably a lot of male gamers did, worrying that my favourite games would be attacked and deemed atrocious and sexist. But rest assured, that's not happening. I'm looking forward to the rest of the series.