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).