I really like where you're going with this--the cat, the story, the planned mechanics, the concept art, and the level design are all very nice!
I'm having trouble pointing the camera where I want it in the prototype though--it would help if the cursor locked ("Cursor.lockState" in the Unity docs) after clicking, to stop it from leaving the area where the unity build can detect mouse movement. The mouse sensitivity/ camera motion also seems a little high for my trackpad, though it does kinda help with the lack of cursor lock.
Thanks for providing a web build!