That's SUPER weird because for the most part, I don't really see his legs as tied together. I don't know if it's different horses, but the one being more "calm" and doing a steroid version of the piaffe obviously has free use of his legs. The one who is freaking out and trying to lay down doesn't appear to be really "restrained".
If I had my guess, these animals (animal?) seem to be severely abused and neurotic. They're jumping out of their skin, and getting so worked up they can't even think about what they're supposed to be doing. Which I think is the point, because somehow crazy horses look "spirited" and "free".
There's definitely something around their legs at least, but now that MM mentions it there are parts where one of the legs moves quite independently from the other.. so perhaps they aren't actually tied together.
Either way, whatever is going on with those horses is saddening.
MM I think you are right, its hard to see because it is poor quality video. I don't think his legs are tied. I just can't figure it out. It does look like 2 different horses in the video? There are a lot of "dancing horses" on youtube.