One (entirely valid) criticism is that not even an error message popup appears. It should be the case that a GUI error message is displayed if Zenity is installed. So a simple thing to do would be to add Zenity as a Suggests: line for the package.
If you instead go with the .desktop approach, please bear in mind that it's not just /usr/share/games/doom you should check - there's also /usr/local/... and ~/.local/share/games/doom. -- Simon Howard https://soulsphere.org/
