There is a recent trend of 'serious games' which use video games to teach and train people in various capacities, including military, health care, management, as well as the traditional schooling. I see no reason why this couldn't be applied to rationality training.

I always liked adventure style games as a kid, such as King's Quest or Myst, and wondered why they aren't around any more. They seemed to be testing rationality in that you would need to guide the character through many interconnected puzzles while figuring out the model of the world and how best to achieve the goals of the protagonist. It seems like the perfect video game genre for both developing and testing rationality skills.

Specifically, I've thought of a microcosm of the real world, taking place in a different setting yet similar enough to our real world that there would be analogues to religion, science, politics, etc. As you progress through the game, say from child to adult, you learn about the world and see how different beliefs and strategies effect the game. Players would encounter similar challenges to the real world but be disconnected enough not to put up a defense mechanism, yet involved enough to care about the outcome. Add MMO et al features to taste.