I believe its an option when you right click the game in steam.
If you don't want the desktop icons, you don't need to relax the flatpak permissions for the xdg-desktop. Just the first two for allowing steam to see the icons and the applications folders.
If the right click option isn't there in steam, there might be a way to regenerate the icon, but off the top of my head I'm not sure. Reinstalling the game should do it but that's a pain for larger games.