So, I think this is plausibly a Cinnamon or Mint bug - Cinnamon is setting the XDG_CURRENT_DESKTOP flag to X-Cinnamon, which is OK, but gnome-terminal.desktop (and probably other things) specifies OnlyShowIn=GNOME;Unity. Thus, Do (correctly) fails to show it.
Possibly the correct solution would be for Mint to patch the GNOME Terminal desktop file to add X-Cinnamon to the list of desktop environments to show in.
We could also bodge this in Do by treating X-Cinnamon as GNOME, but that's ugly and fragile.
So, I think this is plausibly a Cinnamon or Mint bug - Cinnamon is setting the XDG_CURRENT_DESKTOP flag to X-Cinnamon, which is OK, but gnome-terminal. desktop (and probably other things) specifies OnlyShowIn= GNOME;Unity. Thus, Do (correctly) fails to show it.
Possibly the correct solution would be for Mint to patch the GNOME Terminal desktop file to add X-Cinnamon to the list of desktop environments to show in.
We could also bodge this in Do by treating X-Cinnamon as GNOME, but that's ugly and fragile.