It looks good overall, but I saw a few issues in this demo version:
1. It doesn't properly display attacks when you start attacking while running.
2. It sounded like it was playing two music tracks at once in the graveyard area (it started a new one, while playing the previous one).
3. Some of the blue-clad swordsman enemies moved in mid-air.
4. Text boxes also extend slightly outside the screen at times.
As far as general gameplay design goes, the attacks felt like you had to be too close to hit properly so that I couldn't fight most of the time without taking damage. There are plenty of apples to restore health, but it doesn't feel as satisfying to constantly have to patch yourself up instead of being able to fight effectively. Some of it could just be the attacks not starting cleanly, though.
There wasn't a lot of vertical movement until reaching the town (it's a demo, so that's fine), but I generally didn't have a clear idea of where I could jump or climb without testing it. Sometimes I could jump on a visible ledge or stand on a barrel, sometimes I couldn't.
I also found the background layer movement offputting, since the closest/frontmost background segments move the slowest, and ones furthest/rearmost move the fastest, instead of the other way around.