I’ll admit that a big part of Bioshock’s twist relies on the fact that the player has autonomy. But the way the game builds a compelling world and slowly pieces together a history renders it one of the most engrossing narratives in all of media. A twist surrounding identity is almost always rewarding, if the clues are present, but the surprise is still there. Bioshock is full of hints, as is the movie Fight Club. It really seems like something that could work.
Or, hey, use the world of Bioshock Infinite. That might make for a good action movie that also thoughtfully explores complicated themes.