Streaming from one platform to another is always going to be tricky, for a multitude of reasons. I don't see platform holders allowing this kind of functionality, instead of just buying the game itself on their own platform. They don't like that kind of competition.
That and with this whole streaming gig, it's obviously going to require it's own power to run said games, unless this service is going to oeprate like Nvidia, where they run everything from some top end machines, and you paying a chunky sub fee to run said games.
I just don't find this practical tbh, especially for said games that run better with K+M.
Also we already have Steam Link anyway, with Steam being the main client with the most games out there.