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I think it would be very possible to use a wiki as the primary, if not the exclusive, web site/resource for your game.

How often to people actually visit the web site for games they are actually playing? Unless the web site has constantly changing content, some kind of helpful tool, or anything of that nature, I will never go to a game's web site once I am playing it.

A wiki can very easily, and perhaps more efficiently, make tools and content available to players.

PHP Nuke made setting up an "active" web site pretty easy. You could do pretty much everything those sites did via a wiki - and perhaps do it more easily.