Awesome this! Somehow this triggered so many questions in my mind. "What's the best moment to worry about time?", "What about if I gobble up as much time as possible at the start?", "Provided you have a lot of patience, would you be able to let this game go on forever?". In other words, far more tactics can be applied as I would've imagined up front.
Apart from that, it plays really nicely, the soundtrack is awesome and the ramp up in difficulty is also really nice. Also, it's much harder than you think to find which cat you control. You start to wonder which movement pattern is easiest to detect.
Man, I am impressed with the depth in this simple concept, well done!