these people need permission from a massive corporation calling it something other than Linux so they can dodge the cognitive dissonance of hating Linux

A few things:

1. It gives manufacturers a blueprint for their devices. You will see a lot of handhelds running SteamOS from different manufacturers. You will also see a lot of small "gaming boxes" with SteamOS to plug in your TV. That's great!
2. Game Developers will have one distribution to test their games on. One of the bigger problems linux had before SteamOS was the big clusterfuck of different distros. Great for users, but a big headache if you're developing for it. Now you can say "it runs on SteamOS", test on SteamOS and you don't have to deal with bug reports from people running RedStarOS
3. It's Valve. It's a company. They are the biggest store selling games and they are building their moat to protect themselves against Microsoft, Apple, Epic & Co. That not exactly great for users, but also explains why Valve is doing this linux push. To prevent Microsoft from abusing their Windows monopoly to crush them

I think it's mostly a matter of having it preinstalled.

The perception is that if it's pre installed, then it is designed for the device.

Consoles have accepted keyboard+mouse for years now! Microsoft started with the Xbox one and Sony started with the PS3; Though there were select games for generations prior that supported k+m through their own implentations