I'm thinking more specifically of "parlor game" formats, because that's a situation conducive to a rich exchange of ideas in the debrief. Single-player games are interesting as well, but all I usually get from them is some recombined version of my own thoughts and insights.

There is something uniquely interesting about small-group discussions around transforming ideas: I find that every person in the group has seen things under a slightly different angle, and most of the time one or more participants have thought of something I would never have considered on my own.

An Internet discussion forum can work to some extent, but my favorite games tend to involve some kind of physical tokens or game pieces - possibly because I favor the kinesthetic modality for learning.