Ok.. so what genre was this again? There's not enough story to be an rpg, not enough getting lost to be a maze, so I suppose it's really just a 'puzzle game'.
If I think of it like that, it's not a bad game. Although your puzzles don't reset, they do seem to have ways to move themselves around if it gets stuck. I wouldn't say it was a challenge, but it does work together.
As a complete game, it's lacking. There's no intro, so I have absolutely no idea what I'm doing here, and only sort of realised what the plot was when I got a message at the end of world 1 telling me I've cleared it of evil. I don't really know what the purpose of your battles were, there's very limited healing items, 1 (?) skill, and none of them go on for more than two turns. It seems like it was more, 'hey try to avoid this map sprite' or 'here's a change of scene' than an attempt at interesting turn based combat.
I didn't even notice what any of this had to do with 'following the map'- the first time I picked it up I didn't see what happened since it's a player touch event. I tried to walk out of the portal room and got stuck on the first map where I couldn't move. So, what's with the map? Is that an alternate dimension? We don't actually get a map item in the inventory either.
The last world was so anti climatic. You can actually just walk onto the portal and return to the title screen without finishing the demo. I can make a guess that this guy was the 'evil dude behind it all', and sometimes it's ok to have a story like that where things are slowly revealed to you, but you need to have something at the start or early on to actually grip the player and make them want to continue.
My advice to you is to figure out what you're trying to make. Is it just a puzzle game? If so, you need to do some optimisation of menus etc to make it not look like a forgotten rpg. I'd probably take out the first map, so that you have the portal room as a sort of 'level selector' and the rest of the worlds are acceptable as cartoony puzzles instead of seeming like a poor attempt on a realistic world. Is it an action rpg? If so, you need to use an abs rather than turn based combat. You also need to set up some kind of backstory or explanation. Is it a maze? Then you'd need to make things bigger/players view smaller. The point of mazes is getting lost and trying to find your way around, which you don't get when you can see the entirety of the map.
So this review might seem harsh, given that the game is not bad, and as far as I could see, you've managed to avoid any game ending bugs by getting pushable objects trapped which is a huge achievement. But since this is a demo I hope that you might take this feedback on board and focus on what you have and what you want to make before trying to expand further. Hope this helps!