There's 3rd party software like OpenALVR (FOSS) and Virtual Desktop ($ but works better IMO) that let you stream PC VR games wirelessly
I'm using Virtual Desktop and it works flawlessly with Alyx. It's so puzzling that you need to enable developer mode and sideload stuff to enable wireless while they allow you to connect with a cable out of the box.
Is there a tutorial on how to get alyx running like you describe?
I used ALVR and found it quite easy to get setup with + its FOSS which I prefer
https://github.com/JackD83/ALVR is the fork to use, its instructions arent super indepth but I got there its not too hard. And then steam views it like a regular steam vr headset. Its pretty cool.
There are a bunch of good tutorials out there. I don't remember which one I followed so I can't recommend anyone specific.