I think the YouTube description makes it obvious the OP thinks this is admirable behavior from the horse and rider. I think it is very obvious it is not. I don't know how anyone can watch the horse and think the horse is content with being ridden like this.
I don't think the OP needs to be told she is leaning back, or bouncing, or pulling on the reins. I think this post:
So you think the "flopping" is hurting the horse's back? Do you think its mouth is hurt from the bit? What about the horse's gait?
indicates we're supposed to admire the horse's gait.
Also, the YouTube has this comment from the person who posted it on YouTube:
"Look, I appreciate your concern, but wish you would watch a little closer and read the video description before commenting. There's no abuse, no pain/harm to the horse, and only a few minutes of goofing-off bad riding to this. The point? Fun for the rider and horse, and good exercise."
Sorry, but I'm not sympathetic. I see bad riding making a horse unhappy, and critiquing the leaning back won't help. The riding seems to be intentional, with no regard for the horse's response other than "sometimes she can rock it much harder than this. Check out that flailing pastern action."
The title of the thread is, "What do you think of this horse and rider?"
I think the horse is unhappy and the rider is causing it.