The answer is one dll that gets loaded that causes the game to crash on startup. Go to $WINEPREFIX/drive_c/GOG Games/Cyberpunk 2077/bin/x86/ and rename GameServicesGOG.dll to GameServicesGOG.dll.bak (or delete it if you like to live life on the wild side). Now enjoy playing the update!
This was tested on Arch using AMD and latest mesa.
What is the purpose of that DLL? I ask because the Steam version is also DRM free (can be run without Steam), but lacks that DLL.