I have a working alternative to Gamestream - both Server and Client, written in C++ - lying around here. It's just that I could never figure out how to monetize it, so now I'm just using it for me and my friends.
But when testing it, I noticed that quite a lot of competitive games will consider it "cheating" if you try to grab the screen in real-time. I presume that's to avoid AI-based aimbots who would actually just recognize the enemy based on the picture.
Also, some games outright forbid using game streaming services in their EULA, which is how pretty much everything by Blizzard & Activision got booted off Geforce NOW.
And if you think about it, it does make financial sense for them to forbid streaming. As-is, I am sharing one purchased copy of the game with my friends. We have one cheap GPU server with Hetzner and we take turns playing the games. Or we play a couch-coop game online with multiple Gamepads connected to that one server. If you prevent this form of sharing, each of us would have needed to purchase a copy of the game to install locally, so the publisher is potentially losing money by tolerating game streaming.