Very nice game! I like the idea of only being able to move each direction once. Originally I was thinking something similar but instead you'd only be able to move in one direction but it didn't play as well, this is much better. Something I would suggest is to allow the player to not have to hold a direction making it so they can take time with their movements, maybe only lock them out of going in a direction once they change directions. It would also be nice to be able to see the path of the enemies; I found the ones without enemies much more enjoyable because it was predictable right away where as with enemies I didn't know which way they would go or how far until I messed around a bit.
All together still a great game!