Yeah, my statement's only true in certain senses. It might be more accurate, with tabletop games at least, to say that games are a UI to the other players - that is, they channel social interactions in certain ways.
this is my feeling. the games that last are ones that distill some aspect of friendly competition between people. and the very best games are the ones that cause you to interact with your friends in some new way (games that involve auctions or mini-economies tend to do this well)
