Isn't this already happening? I stream games to devices around my house from my office where I have my desktop, and a small Debian server as a media server, mumble hosting and the occasional chivalry or CoD4 server with friends. I get that the server has a bit of a barrier for entry, but the game streaming, that's just Steam. Granted you need some kind of i386 or x86_64 device at the streaming end that can install steam.
Yeah, it's technically here with media servers too but the barrier for entry is still higher than your average Joe will bear. The idea of an out-of-the-box solution has been tossed around here a few times I think; a little server that manages networking, storage and other services for your home. One that just works after a simple gui walkthrough for setup, and doesn't make us so dependent on cloud services that exist to sell advertising space.