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There's a Chess Module, but no other games modules that do what you're asking. I've never used it, so I don't know what features it has. The closest thing to a multiple games module is a really basic module which basically consists of an iframe to another site's list of games. When you click on a game, a pop up windows comes up and the users can play the games, but the pop up is from the external site, there's no score tracking. The good thing is there are 407 flash games to play, but no score tracking, so I guess it depends on how important that part of it is to you.
