Huh, even though the game sucks on touchscreen, I just tried it on my phone anyways.
Apparently the spacebar doesn't work/glitches out when trying to play through animations and stuff.
Just use literally any other key for that and it works.
Edit: Due to phone's autocorrect crap going on behind the scenes, you still might want to hit space every now and then, at whatever points you might want to 'save' your progress, otherwise backspace may happen to jump way back, potentially to the beginning of the game.