Streaming, no. One simple reason: Latency.
Nintendo cares a lot about latency. This is why Nintendo put a lot of effort to keep WiiUs gamepad streaming latency to as low as possible. Even though other streaming solutions are good enough (ps4-psvita, tpc-tablets, etc), they wont be as good as something designed from the ground up for it (like WiiU).
The feel of the game matter a lot to Nintendo, how you press the button should affect how Mario jumps, there was an article on gamasutra about this, something about milliseconds and Mario's jump.
This is also why you see patents like Supplemental Computing Device, one of it's biggest advantage is latency. It makes (near) real-time cloud computing much more practical.