You don't need to extract an `.appimage`, you need to mark it as "executable" (if it has not been marked like that already) and run it directly, either via a terminal or double clicking the file in your file-manager.
If that still does not work we probably want more information (like the openxcom.log file or any messages you get when trying to run the app from a terminal).
P.s. No experience with steam deck, let alone the desktop mode, so my help can only be limited.