Wow! The aesthetics of this game are awesome! It has an awesome vibe that I immediately fell in love with. I think the concept has some nice potential.
A few things I noticed. There's nothing besides curiosity that make you fight the monsters. And after beating some it even seems that I don't get anything in return. These should be very apparent to the user in order for them to continue to want to play.
Design-wise, I would have loved to have more insight into what each square type does. From what I've played, it seems each terrain gives you some boosts/handicaps which can be useful in battle. Sometimes I go and eat stuff, but I don't know what exactly it does.