The map doesn't show but I guess I don't really need it to solve the puzzles?
The map shows in a different browser, there's no map when playing on Chrome. Also, the character won't step on the lights, but will just appear in the other side if you move twice in that direction (also just Chrome).
I'm a bit stuck at the moment but I liking the game a lot! I can plant melons now :P
I think the reason for not being able to see the map is whether or not you're letting the browser store data. For me, incognito mode prevents the map from working. Whenever you're on a door (for example, when accessing the map) the game tries to save your progress, and if it can't, I guess that the turn just isn't shown properly, making the map inoperable.