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In theory, it should be possible to install a 64-bit operating system in a virtual machine, provided you have a suitable processor.
However, I'm not sure if you'll be able to play games on it. Virtual machines are inherently limited in terms of memory and resources, and you'll have to find a way to allocate them between the virtual and real machines (at the expense of the latter). Also, if you have a 32-bit operating system, I don't think the pre-installed hardware will be able to handle such complexities.
Besides... After all, you still need to install an operating system in the virtual machine, so why not install it on the real machine? It might not be worth it for just one game, but I think this won't be the last time you have similar problems. New games will likely require this more often.