Is it possible to recover a runner's inputs from their gameplay? Otherwise, how would we even know for sure they are playing the game and maybe skipping a frame or two here or there?

It is not possible to recover inputs from gameplay unless you were to recreate every frame by using a TAS, which would basically be pointless due to how long of a process it is.

There are many ways that cheating can be detected, skipping a frame can be detected by audio or by using a frame counter.

Player input can only prove cheating if the inputs do not match what is happening in the game, and due to the numerous other ways cheating can be detected, it’s not worth requiring for run submissions.