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Although in all honesty Naughty Dog used Lisp to write their own compiler from a Lisp-based DSL into highly optimized Playstation assembly, and then wrote huge chunks of the game in that.
Which is a little different from wanting to learn functional programming by writing a game. ;)
I would actually recommend taking a look at Flash. With ActionScript 3, you can write your game a very functional style - arrays have map and filter operators, you can get events and pass them through chains of filters, etc. And then you can just publish your game on the web for everyone to check out.
And by the way, you won't be able to do pure functional game programming in any language. At some point you'll have to bottom out in modifying display state - whether opengl calls, or directx calls, or flash display list changes.