If anybody out there seriously starts working on such a service, let me know!
My rig is about 7/8 years old and I've only upgraded the video card when I had to. I'm looking at building a new rig just to keep up and a "cheap" one comes out to $800 for me. Something like this would be very desirable. I would love to be able to shoot this to my main big TV and only using my Chromebook to access it.
Sony et al probably have more specific patents for their own setups, but to the extent they cover this setup they'd either be obvious, or they'd be trying to sue you for doing stuff covered under nVidia or Valve's patents. This, alas, doesn't necessarily protect you, but would certainly raise some PR issues. Plus Amazon might have some questions as well, since they don't want people getting hit for using cloud services to do things; anything that smells like special cloud licensing just because you're doing X "but in the cloud!" is going to hurt their business model.
I can't guarantee they have nothing to sue over, but the costs/benefits would not seem to argue in favor of Sony suing.
On top of that hardware costs vs performance along with hardware h264 encoding is getting cheaper.
Almost no one will pay for laggy games at last gen resolution.
The thing that I would worry more about when running a service like this would be liability for what users of your service do / say.