Gravity is not necessary otherwise self winders wouldn't work in space. Inertia is enough. A slight movement clock wise or counter clockwise then stop and the rotor would continue to move in that direction until resistance from the spring overcame inertia. Those movements that wind in either direction could be turned in one direction then the other.
Gravity can add power to the rotor but also bleed power away from it.
As I remember it, and I might be wrong, the table also rocked slightly.
If the table in the film is a mock up the basic design could still work in real life.
PS thinking on it a bit more I'm wondering if the rocking motion may have come from the table being raised from vertical in the closed drawer to horizontal when opened for easier access.
I've also seen a winding table where the watches were laid out flat on a felt cover, the table both oscillating and rocking very slightly at the same time. I Don't remember what film that was in.
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