The game you tried out was a game jam entry made in a rush thus is not properly tested for mobile (Thanks for trying!). I was referring to my other game that's in development shown in my question.
As for your case, I think these might help:
- Try turning off auto detect size and set the resolution manually.
- Enable itch's "Fullscreen button". As previously mentioned, Unity's fullscreen button (blue) simply resizes to whatever resolution your screen is, itch's fullscreen button (white) is what allowed me to play my game on fullscreen.