No.
An operating system should be just that. If you want a version of Windows bundled with Office, great, but the OS should be exactly the same in both cases.
As for "useless services running in the background", while many might not be necessary, most users won't know which usage cases would require which services. You can open up a list of all services and decide which you don't want to start, already, but presenting users with this choice is pointless. If you're thinking "for the games, just remove all the ones that gamers don't need", then just stop. Gamers use a lot of services, even ones you'd never think games would use.
Do you know which services are used by all game DRMs out there? Which services are required by emulators? Which services are required by virtualisation? Which services are required for syncing all this with your 3D TV? Which services are required to handle the decryption of your blu-ray movies? Which services are used to handle the authentication of that? I could go on and on, but I'm working so must cut this short.
Thinking that a "gaming OS" would just be "OpenGL drivers and something to let you add hardware" is very short-sighted. Our modern systems are fairly complex as are our modern games. The tools used by developers require far more of the OS than you can imagine, and if you think Windows loads a bunch of useless services, then I suggest firing up SteamOSwhich *is* a dedicated gaming OS and look at just how many processes it requires.