No gear levers either. It's a fixed gear. The cranks are turning as expected.
It looks like it's a one speed free wheel. It could be that the video is breaking up but it looks like the crank is not spinning as fast or as smooth as a fixie would.
I checked for that, but there are also no brake levers.
Indeed they're turning at the same rpm before and after he takes his feet out.
Also, he drags his feet on the rear wheel to brake before he puts his feet back in, I didn't notice that at first either.
No reason you couldn't do this stunt on a freewheel bike with brakes ... but it's a little more impressive on a track bike.
I think I've seen somebody do this on the Champs stage of the TdF... in between the champagne drinking and other antics.