Streaming over the internet is okay, but it's SO dependent on your connection quality (and your bandwidth limits). It can work, though, obviously.
Maybe it'll work in the future, but it's a pretty poor experience right now.
I have the original NVIDIA Shield, the one that looks like a 360 controller with a screen strapped to the top. Late last year they announced a free trial for their GRID cloud gaming service. One caveat was that their servers were all in San Jose, and if you're too far it warns you. I tried it from my home in Illinois, and it was predictably horrible with just a ~70ms ping. I tried it again from California and it was only slightly less horrible with a ~20ms ping.
Driving games become drunk-driving games. Another driver comes in and hits you? Good luck recovering. Forget that there's a turn at some point in the track? You'll never react to it in time. Things that require constant micro-adjustments like drifting are virtually impossible.
Fighting games become button-mashers because you can't react fast enough to block or counter-attack.
Seriously, these were launch titles! I assume 99% of testing happened with local-network latency. If I were the guy at NVIDIA who okayed go-live, I'd be deeply embarrassed.
The only thing I'd use it for right now might be a turn-based strategy games, or other things where latency really has no effect on gameplay.