Actually, he isn't interfering. At those heights you'll be bumped off. He is holding on and balancing on his knees, working hard to not interfere. Think about it--you CAN jump bareback, and you cannot push out of the way with your stirrups, then, hence the wisdom of learning to jump without them.
First photo, slack rein. Second photo and third photo, contact, happy horse posture (ears forward.) These courses are tough and the rider has to make changes often as soon as the horse lands bc you can't communicate the order of the jumps with your horse ahead of time.
Something else, a good jumper will take you with him. A poor jumper will throw you up when you jump. It has to do with the horse being able to "couple" or get the hind legs way underneath before the takeoff. Poor jumpers jump everything flat.
If your only jumping experiences have been on a poor jumper, it's like the difference between driving a clunker over the RR tracks, and driving a Mercedes on a smooth road.