I also find it perplexing that this whole thread is about Anita again, even if she is neither part of that institute nor author of that study and did little more than a bit promotion and being part of some hosted event.
She is irrelevant and also a troll. Her whole relevance comes from purposefully provoking people. Ignore and forget her.
OK, quick question.
Do you think it's pure coincidence that it's so much more frequent that the women needs saving and the man does the saving?
Meh, there are more than enough saved men to be saved. I could not even say whether men or women get saved more often nowadays.
But where i still see a big difference is, what kind of men/women get saved. Saved men are ususlly 1-scene minor NPCs, saved women can more easily be major characters or squad members. I think there is still a notion that "needing to be saved" is more a stain for a man than for a women and not something they want to put on major main characters that much. Putting this on minor male NPCs however makes the protagonists seem even more badass in comparison.
But that is just some impression, i don't have numbers for that. Still, it feels less like pushing women in the role to be rescued and more like a limitation on the kind of roles major male characters can have. Which already tend to be far more uniform and restricted than major female characters.
As for the person doing the saving, well, female protagonits are pretty common and even more common is having both options for the PC. And i don't see much more saving in games with male protagonists than in games with female protagonist or both options. And while there might still be more of the first than of the second, they are not actually treated much differently.
I am pretty sure the damsel trope is far less common in games than in firm or TV. I have a hard time remembering the last time i have seen it playrd straight in a game but can instantly remember several TV show examples from the last half year.