But a cat free-falling from a height is also weightless, and yet they manage to right themselves using perceptual cues. The point of the experiment is to see how the behavior changes when the sensation of weightlessness is presented for an extended period of time, without the "falling" motion (relative to the perceived local environment) that normally accompanies it.
The cat's system has memory. The transition into free-fall from a state where it was previously experiencing ground reaction force provides a cue for the self-righting reflex on the direction of "up/down". Apparently even blind cats can self-right based on their vestibular system.