The article I read didn't include the video, but horses are extremely sensitive. They'll completely alter their direction or come to a dead stop with just a slight shift of the rider's seat bones, and what doesn't look like a punch to you would feel like a major assault to the horse. In fact, what the coach did WAS an assault on the horse because it was simply a factor of the coach's emotional state, and the poor horse was given the brunt of that.