Now, as far as I'm aware, there are a relatively small number of the "big" games published for Linux- Unreal Tournament 2004 is available for UNIX based OS including Linux and Mac.
It is possible to run Windows native software on Linux, using a compatibility layer such as WINE (stands for WINE Is Not an Emulator), or "Cedega" from
http://www.transgaming.com/, which is specifically targetted at games (and I think it's based on WINE). Bear in mind though that Cedega is subscription based. I checked their site, and it's about $5 a month. Alternatively, if you have a very powerful computer, emulation is an option, installing Windows on a virtual machine then running games on that. Of course, that isn't really running the game on Linux, it's still running it on Windows, and on the whole, this is probably too demanding a solution on the hardware compared to a compatibility layer.
On the other hand, since I assume you have already got Windows of some sort in order to play the game you mention, so you don't really need a Linux based way to play your windows games
EDIT: Beaten to it anyway :P