Depends on which direction it's spinning. You can spin in a way that the antenna keeps pointing at the ground (but rotating, which would not affect it).

You can actually see the video feed blip out once per revolution. I assume it's because the transmitter is briefly pointing away from the receiver.

What's the bandwidth of the video and transmit rate of the antenna? How large is the video buffer?

We haven't had to rely on a 1:1 record->transmit system for about 50years now. If the antenna has more bandwidth than required then a few seconds of connectivity each revolution may be enough to give a perfectly smooth video signal.

An omnidirectional antenna on the satellite, a high gain large dish on the ground tracking the satellite across the sky, and error correcting codes that spread errors over time.

Combine those things together and you get a pretty large section of the original signal intact.