Even the Frame doesn't support Linux properly. You cannot do streaming from a Linux machine, it must be a Windows machine. (yet).
I'm sick of pretending Valve cares about Linux. Their own games have major issues with Linux.
Every CS2 update breaks something, last time it was the inventory screens which were completely broken for like 2 weeks.
Left 4 Dead 2 has major frame pacing and stutter issues on the Native Build & Proton doesn't let you play multiplayer.
Counter Strike Dev Tools only runs on Windows.
You can't stream from a Linux box to the Frame? Where did you hear that? Given that you can stream between Linux boxes using Steam, I find that surprising.
Linus said it on the leaked TechQuickie video from a 2 days ago.