It's called gymnastics and is commonly used in training young green horses it serves many purposes when training a green horse such as rounding his neck and back and keeping him balanced.
In my 9 years of riding jumpers I've yet to see a gymnastic that involves running the horse into the arena fence. And funny you should mention rounding his neck and back and balancing him because when she runs him into fence he hollows out and falls off balance, makes a very unbalanced, stiff turn, and then is forced into cantering over the fence again in a mere few strides. Also, in my experience, gymnastics typically involve more then one cross rail. I've often used gymnastics to improve a horses carriage by encouraging them to keep impulsion and pull their knees up to make it through a line of 2-4 jumps or ground poles. So no, what you have here is not a gymnastic, it's a cross rail.
I'm sorry, it's your money and you can choose to train him as you like, but in my experience you probably aren't going to get very far in any competition, recognized or unrecognized with a horse trained in this method.
Why not establish a good working canter on a 30m circle, have him balanced rhythmically and with a good forward impulsion, then keep him straight off the circle at one point, canter him calmly over the jump, regain a good canter on a circle again, and bring him back down to trot.
Watch the video for yourself, driving him into the fence did nothing but make him annoyed.