The door seems to be bugged.. if I interacted with it before completing the level's goal, once I had completed the goal I could no longer interact with the door.
A really neat idea but the execution is ultimately kind of annoying. Having to click "End Turn" after moving one square every time got irritating quickly, especially when there were no enemies on screen.
The lack of animations and sound make it very hard to tell what's happening between each move.
Something to consider might be using the rules of chess to help you set up safe attack moves. For example, attacking a pawn from the side you'll take no damage but if you attack them from a spot they can move to in chess you'll take damage as well. Because you take damage every time you attack, as it is it makes it nearly impossible to clear the full dungeon.
What you did though I thought was pretty neat, I think the idea has potential