I can pick up my Steam controller and play on every display in my house thanks to Steam Link.
I 3D-printed a backplate for my Steam controller that mounts my phone to it.
I did this to stream Final Fantasy XII to my phone back when it came out on PC. It was amazing. It was like a straight up handheld version,at 60fps and 1080p+, with fully custom controls that even allowed me to enable and disable cheat engine scripts (like 10x speed and 'always rare drops/steals when available') on the fly. And no latency*!
(*i'm sure there was a little bit of latency, but it was unnoticeable. and i don't mean the sort of 'unnoticeable' that remote play enthusiasts used to claim, i mean it literally)
I threw that mount away a few days ago.
I don't need it anymore. That's because Steam now supports using my cellphone screen itself as a fully customizable input device. I can play FFXII on my phone like it were a mobile game. I can customize where the little circles that represent my analog sticks go and all that jazz. RPGs on PC are never gonna be the same for me :p
So yeah, when you say every display, you really mean it.