I really hope it works on Linux. When I last tried ALVR I had a few issues, but I've been wanting to give it a chance once again. More options would make the whole thing a lot easier though.
According to the minimum specs it requires a Windows 10 or newer, and an Nvidia GPU.
As of now SteamVR itself is in a woeful state on Linux, maybe that's why they don't list Linux support for it