I can only assume you would use data loss prevention software/techniques for tasks this. Locking out USB ports and logging web traffic on the terminal would be the first step but there's probably smarter things you could do.

True, indeed. If you want, you can somewhat prevent.

Although, to be honest, typically videos are buffered and even cached from the browser, so logging incoming web traffic won't help there.

Preventing outgoing traffic might help. Preventing storage would be interesting. I think those machines need to be really just terminals where you can't do literally anything but click yes/no and go to the next in the queue. It'd be interesting to know how they do it.