playing this without really thinking it through, so my remarks may be off.

the mechanics are unusual in the sense that they're deceptively simple but cunningly difficult at the same time... challenging.

becoming stuck (in level 3, e.g. when reaching the spaceship without the key) is annoying. could be that you intended this, but for a casual game it would feel better if that couldn't happen.

related : having to grab the mouse to click the 'replay' button is annoying too. maybe just use a key ? same goes for the 'next' / 'prev' button. when the spaceship flies away it triggers an annoying (growing) scrollbar at the bottom of the page. some overflow: hidden missing somewhere ?

overall I like the concept. someone else already suggested making the board larger, which I completely agree with.