Who is the audience and what are the desired outcomes from playing the game?
I can guess, but it is better to outline these things explicitly at the start, lest you wind up with something that no-one wants to play.
As for genre, I immediately think of something like a role playing game. I think back to FFVIII, which allowed you gain, increasing your salary when you took in-game tests. More recent RPGs that have huge volumes of information in in-game encyclopedias (games like KOTOR 1 and 2, Mass Effect, Xenosaga, etc).
I would consider using a plot similar to the Harry Potter fanfic, such that your character starts off in a non-rational place, and advances using these techniques. Techniques and studies are mentioned in the dialogue, and full references become available in the encyclopedia as they are mentioned.
This sounds like a really interesting idea. I have always wanted to design a game. Sadly, I just don't have the time (or the knowledge).
I know there is interest among this community in building rationality oriented games as teaching tools. Today we announced Steam Greenlight. We're essentially turning the game approval process over to the community. It may be possible for quality rationality games produced by the Less Wrong community to create enough gamer-community interest to get placed on Steam for distribution.
http://steamcommunity.com/greenlight
I feel that this creates a better opportunity for rationality games as teaching tools to find broad distribution than if it had to go through the Steam product review team. Ultimately, it shifts the responsibility onto the games' creators and their community to create and drive interest for the product and it removes our limited decision making from the system.
I'm posting this here for awareness of this possible avenue toward reaching a broader audience.