All you need to do is download it from GitHub or Mod DB, and place it into your Alyx install folder, overwriting the existing files and then set "-novr -vsync" as a launch option and yup — it works. The screenshot below is it running on my Fedora KDE desktop, with Proton 7.0-6 and MangoHud as well. I've only tested with Proton, as the Native Linux build hasn't work for me for some time now.
Speaking in an update on Mod DB the developers of the mod said: "This is our biggest update yet and we have no plans on slowing down! With thousands playing Half-Life Alyx NoVR we are happy to announce our largest update yet! As the titles state the entire game can now be played from start to finish, with the Gravity Gloves fully implemented along with combine fabricators providing weapon upgrades. Also since we are now updating the final parts of the game there may be spoilers! We will do our best to not spoil anything while ensuring we communicate these late game areas have been updated along with their gameplay mechanics."
They do still have a whole bunch of stuff left to do, but it's quite impressive what they've been able to achieve. You're also not currently able to get some of the Steam Achievements but it seems a lot of them are possible now (33/42). Even some popular mods for Alyx are playable with this including Levitation, Extra-Ordinary Value, Belomorskaya Station and Overcharge.
You can see in the shot below of Alyx running on my Steam Deck too, and there's even a Steam Input configuration ready for it and it felt quite playable.
Half-Life: Alyx in VR is one of my all-time favourite experiences, so it was thoroughly weird going through a little bit of it with this mod.
You can see some of their videos on YouTube full of spoilers of course.