What videogames should be taught at school for literature class?

You're missing what makes the video game aspect of Bioshock important. It isn't that it makes the experience more personal, it's that the player is used to doing things in a video game just because an NPC tells them to. A book or movie that tells that same story could reasonably make you suspicious of Atlas; this is a dude, after all, that tells you to murder little girls. Bioshock exploits the typical video game setup which has you intrinsically trust the voice in your ear giving you the next objective and makes him the villain. Might not be too wild nowadays, but it was a fairly big deal at the time.

And I've never played Baiten Kaitos so maybe I'm off, but your description of it and the claim that it wouldn't work in a book is kind of funny. There's a famous Agatha Christie novel where the protagonist does indeed turn out to be the murderer, making him the villain of the book.