If the earth would not be rotating there would be no geosynchronous orbit because then as you mentioned anything would fall down as it has zero orbital velocity. But as earth rotates once in 24h you can have something orbiting above the same spot on the surface.
Orbital speed depends on your height, the higher up, the slower sideways you need to go to stay in orbit, so any rotating planet has some syncronous orbit, its just higher or oowed depending on a days length and its mass.
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