Unfortunately, try as I might, I just can't get this to work on the Steam Deck. The appimage works fine when running it directly in desktop mode, but it refuses to run when added to Steam as a Non-Steam Game, and as such won't work in game mode. 😢
I'm pleased to announce that I finally managed to get it to work. There's just two things you need to know to get the native Linux version running on the Steam Deck:
1) Make sure the filepaths are correct. BoilR messed this up when importing the game through itch, I had to go to the game's properties in Steam and manually browse to the appimage again for Steam to fill in the correct filepaths.
2) You need to use "--no-sandbox" in the game's Launch Properties from within Steam.
And boom! Works perfectly fine! I personally recommend changing the left joystick in Steam Input to mimic the d-pad, so you can use both the d-pad and joystick to move.