I don't believe the game servers are actually normal servers. Linux by definition is a server because of all of the server software included, although you can use it as a client/desktop.
From people that I know that have set up game servers, they usually just grab an old PC, slap Linux on it, install the game server software and throw it in the DMZ on the corporate firewall cause they usually have a T1+ and the big wigs never know about it.
Linux is the choice because it's free. In order to run it on Windows you need to run the server version of Windows which isn't cheap. The reason you need the server version is because the client version only allows X number of TCP/IP connections. Besides being free, Linux doesn't limit you in any way...