The facebook video does incorporate dressage. There is collection and communication. Just because tricks are added doesn't mean it isn't dressage. It wouldn't fall into the category of the modern competitive dressage. That dressage has rules and guidelines that makes it that way. What about classical dressage? They do spanish walk and things like levades that you could call tricks but that is most definitely dressage. I don't think you should categorize dressage and say something is dressage or not dressage. Yes, it's not the "competitive", but it is dressage. She had some tricks that wouldn't be considered dressage but I would call her riding dressage.
As for the rejoneador(bullfighter), I wouldn't say that is not dressage because it doesn't have the same relaxation of dressage. It follows similar principals, the main ones being communication and collection, but it is also very different. I think the riders and horses are fantastic but I don't agree with the way the bulls are treated and killed.