Interesting concept and use of the theme.
Got slightly frustrated with several sections where it is pretty easy to overshot the required location for a key or exit (e.g. stage 3 key 2). Game doesn't feel like it is supposed to be testing for execution (correct me if im wrong), so perhaps tile-based movement would be a way to minimize such issues.
Again CMIIW, but several puzzles require the use of precise movement in between what appears to be 2 tiles on the map to complete the level. This kinda felt strange to me as the rest of the world appears to be in nice spider shaped tiles.