I disagree with that. In the sense that the horse has to perform a prescribed series of movements with subtle cues from the rider with each movement being scored individually, I'd say that's pretty close to a dressage test in theory. Sure the reining horse isn't performing at all three gaits, but they still have to do specialized maneuvers (i.e. Spins, lead changes, roll backs). Plus reining does have collection and extention with the big fast small slow canter circles, and uses cones as markers as well.
Not to mention both reining and dressage have freestyle classes where you can make up your own pattern set to music (don't see too much of that with horsemanship ). I'm not trying to down play horsemanship. Like you said it is similar to dressage in its own ways too. But to say reining isn't like dressage at all just isn't fair. In terms of length of the patter and making use of the entire arena, I'd even argue that it's more similar than horsemanship in many ways.
SO in that aspect, I disagree wholeheartedly....but that's cool.