Not so much bullfighting. That would be the equivalent to rodeo here. Originally it's working cattle.
This working Equitation has four parts. Dressage which is pretty close to Reining, then what's called Manageability precision, manageability speed(the video) and cattle work. Open to all breeds, but obviously dominated by Andalusians and Lusitanos.
What Merlin is doing is Spanish, the "art" of bullfighting. Interesting enough, they mainly breed Hispano-Arabs especially for that, Anglo-Andalusian crosses, since they're quicker on their feet than the straight Andalusian.
I do like the Portuguese bullfighting better, they don't kill the bull.
Ill see if I can find some footage of the Spanish competitions other than bullfighting
It's very impressive how well trained these horses are.
For me, that's the real dressage. These horses are bred for it. They might not have the gaits "who kick lights out", but they're naturally collected.