Tinkering: No Launch button without Proton. Forcing Proton showed the Launch button. Launching the game initiated Vulcan Shaders verification and then a "game running" label next to the game in the lib. Then after a few seconds it just de-labelled with no effect, no processes etc. I tried all Proton versions, all configs from this thread and it didn't run. I reinstalled the game and didn't run.

What helped was to install the Steamworks Common Redistributables from here: https://steamdb.info/app/228980/. Simply pressed green "owned" button and magnet link opened the Steam and the installation proceeded. Pressing the Launch button initiated DirectX installation and the game just started normally afterwards.