For demonstrating the value of the LW-style rationalism skill set, it seems better to you can use it for any mental-skill based game (including poker, chess, life itself even) -- after all, winning in a game, carefully designed to reward certain behaviours does not show us much about these behaviours.

Still, indeed it would be interesting to see some game to train these skills. One thing I'd be particularly interested in to train my skills in making quick yet somewhat accurate probability estimations, and update them when new information arrives.

Another area could be various logical fallacies and cognitive biases - some game that teaches the fine balance between bias-avoidance and bias-overcompensation.