Just a quick note to say that I found out after much experimentation and Googling today that if you try to stream a game from one instance of Steam to another, you may have problems when the mouse pointer doesn’t show up in-game on the machine you’re playing on.
In my case, I had the gaming PC which runs on a projector, and my Mac. During daylight hours, the projector is rubbish for games, as it’s too washed out. So I took the mouse out of my PC and plugged it into the Mac to play on a proper screen. Only, as soon as I launched any game, the mouse disappeared.
It seems there’s a bug in Windows 10 (at least, possibly earlier versions) whereby if there is no physical mouse plugged into the machine you are streaming from, the mouse pointer isn’t rendered on the receiving machine.
The fix: you need two mice. One in each machine, and doing so restores the pointer. Random… kind of counter-intuitive, but it works.