Now that i've seen the video, are you sure that there isn't steak juice on that other dog's backside? In cats social grooming is a big plus. the groomer would lick the other cat (notice the dog laying down was not complaining) until the recipient gets tired of it, but it's a way to get into the good graces of another.
I've had cats that licked themselves raw, that's a very different thing, a nervous disorder, or like bmccasland, they need a job to do, they have all this energy and nowhere to go with it.