Linux is the best operating system for hosting games.
I have been hosting LAN parties at home with 6 computers for years. My Fedora server has been hosting games like: Battlefield 2, Quake Wars, Doom 3, Wolfenstein ET, Half-Life 2 Deathmatch, Counter-Strike:Source, Unreal Tournament 3, The Ship, and more...
The main problem you are going to have with hosting is that the game needs Linux native binaries for the game server. If it does, then you can install and run with a command line. Then you don't really need a super graphics card because everything is running in console.
As for gaming machines, Petch is completely right. Your machine can run Linux, but the best video cards for gaming are the GeForce 8800 and newer. If your old computers can handle that, then you can run games in Linux.
Now I have been testing many PC games in Linux with PlayOnLinux and they run great, but I havn't had a chance to test the multiplayer/networking capabilities. Just last week I tried connecting Titan Quest with a Mint 14 and Windows 7 but they couldn't see eachother. This is going to require more testing and trial-n-error.
I have a unique scenario with 6 computers and a games server. So its rare to find people wanting to do the same thing.