Thank you — that was my fault, not yours. The embed frame was still at itch's default 640x360 with scrolling switched off, so the "Open the door" button sat just below the visible area with no way to reach it. The game itself was fine; nobody could get past the first screen.
I've widened the frame to 800x800 and enabled scrollbars and the fullscreen button. It should work now — you may need to reload the page. Sorry for the wasted click, and thank you for saying something instead of just closing the tab.