Dare I ask why you have a pentagram in the bottom left room? Eh. Nice game! Our cat was a tortoiseshell, so she couldn't be mistaken for anything else. Some years after she was put down, I got a toy with the same colouring, and left it on an armchair. My mother and sister both mistook it for our old cat and were like "What?" when they saw it. Gave me a right laugh, I can tell you.
I'm so used to your interactive fiction that I wasn't sure how to play this at first, but I'm glad I worked it out, because it was super cute. My favourite was the last false cat, the shadow masquerading as a cat shape. Your kitty probably sent its shadow to keep track of you. Did you notice whether it had its shadow when you finally tracked it down? Because cats are mystical like that.