I just installed it from Pamac, as a Flatpak (enable it in Pamac Settings, restart Pamac, search GZDoom), and it works:
This error is expected as I don’t own any commercial files and didn’t add anything where it belongs to run Doom games (as explained in the Flatpak description in Pamac).
Start over explain how you installed it, also you tagged your thread with Snap/Flatpak. It is one or the other, can’t be both at same time. Also always good to give your system info as explained here [HowTo] Provide System Information but first things first… give proper info.