Why do cats like to push stuff over edges and then curiously watch the fallen object? I suggest that they are play-hunting, and are testing the ‘prey’ for liveness & playing-dead, similarly to tossing or poking it with claws.
Good cat toys simulate hunting. The play = hunting paradigm may also explains why cats love to push things over edges.
The question of why cats famously knock objects over is unresearched as far as I know: it’s mysterious, because they often push over the same object as before, so it doesn’t seem to be novel or learning, one would think; but writing it off as ‘boredom’ or ‘randomness’ is not an answer, because there are so many other ways to modify an environment, and this provides no explanation for why knocking-over specific objects is so consistently-chosen behavior.
Why? Because pushing tests the possibility of deceptive prey playing-dead! To explain it, one might surmise that ‘knocking over’ is an explorative hunting behavior, testing prey for information about whether it’s merely playing dead.
This explains why the objects tend to be prey-like in size (with large or shattering objects being frightening), sometimes semi-mobile, they watch the results so intently despite the (to us) predictability, and persevere in it but decreasingly so.