It's a service being pushed because analysts think there's the same money to be made with game streaming as there is video and music streaming.
The fact is though, that the reason streaming works for the other two mediums, is due to it being an entirely passive experience.
Gaming is interactive, and necessitates a perfect, constant connection witch ridiculously low latency, both back and forth, to be functional.
On top of this, the infrastructure required for gaming dwarfs music and video, especially now we're at the point that everyone expects 4K graphics and 60fps as a minimum. The cost of equipng a game streaming server farm, then cooling it and powering it, will be vastly more expensive too, as well as requiring far wider and faster bandwidth to stream.
It's a service not driven by demand, or catering to an untapped market, but being forced into existence by big businesses that have calculated that because apples sell, so too must oranges.
Basically all these companies can make as many competing services as they like, but that won't change the fact that when most pepple try it, it's a bit shit.