This game works with ALVR and Steam Link, but not right out of the box. As shown at the start of the game, you don't even see your pointers, so you have to change the default controller bindings to a community one. The one I chose on the video, from SpartanWarrior, is the one I found most comfortable, although sprinting is a little awkward (you have to double-click the left stick, but click once to be able to walk). You only need to do this once.
Note that at the start screen, another way to skip the two-thumbsticks requirement is just pressing R on the keyboard, but if the controllers are not working the menus will still be unresponsive.
With WiVRn, this is not easy because it cannot use steam input for controls, and there is a bug in xrizer (#149 in xrizer's github) where it makes the game detect the Valve Knuckles instead of the Oculus Touch controllers. It might even be possible to brute-force it by overwriting some game files and doing some black magic to create a mapping, but until the xrizer bug is resolved my advice is to just use ALVR or Steam Link.
Notice that in the past ALVR had terrible performance with this game but this situation has improved a lot, and Steam Link also has acceptable performance, so it's not unplayable by any means.
Versions tested:
ALVR v20.14.1
Steam Link via SteamVR beta 2.13.5
WiVRn 25.9-74-g1dd0ed4 with xrizer
Mesa 25.2.4
Kernel 6.17.3-273-tkg-eevdf
Proton 9.0-4
Gameplay video on Steam Link, including selecting the correct input configuration from Steam Input: https://youtu.be/3aaXq-VPse0
Follow my curator on steam with links back to VROnLinux DB: https://store.steampowered.com/curator/45753882-VR-Linux