I've seen this argument in particular for games like chess and go. The question is how transferable this stuff is. The conventional wisdom seems to be that mastery in something like chess is mostly just learning to pattern-match situations and responses in context of chess games, and doesn't translate to more general aptitude. Though I think the non-transferability studies were about general intelligence, which is very tricky to raise. Studying the rationality skills, which are learnable, of expert go, chess or poker players might be interesting.
I wonder if the abstractness of the game matters here. Picking up analogous patterns to game situations outside the game could work, and more situations might match if the game is very abstract and bare-bones in its model, like go. The default state is probably still compartmentalization, people skilled in the game don't make an effort to unify what they learn in one domain with non-game domains.
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.