It becomes easy to see when watching this clip, exactly how Reiner Klimke became not only a champion in his own respect, but an icon of great horsemanship. There is a thread of modern competitive dressage leaking through his performance, primarily the trot work, however RK is a rider deserving of accolades for his refined and subtle aids.
In particular I want to draw attention to RK's legs… they are quiet, they are subtle. In the extended trot we get a beautiful view of these as the horse approaches almost directly towards the camera. Compare this to modern olympic riders and you will see a stark difference. RK's legs have become one with the sides of his horse, they do not thump at every stride, you do not see daylight between horse and rider. RK also inspires such immediacy in movement from Ahlerich, which is no wonder considering there is no evidence of him overusing the aids which results in a loss of forward and honest energy.
Secondarily, Ahlerich's posture. There are moments throughout the ride where we see Ahlerich's posture fall behind the vertical, particularly in the piaffe and passage. His posture improves however as he is taken into the canter and extended trot. In these places he really shines as he becomes more free and fluid with his balance and posture.
Although his piaffe is nearly free from any forward movement, Ahlerich could be taking a bit more weight onto the hindquarters. His posture plays a role in this quite importantly. With his head dropping down and behind the vertical, Ahlerich has to take little responsibility for his weight placement and comes onto the forehand in these places.
In Summary
There are points where the horse's performance is reduced by the simple fact he loses his balance. It is easy to hide with his naturally large, graceful movement, but the evidence is still there to show that a more effective half halt would improve his trot work and I imagine his already beautiful canter work would have garnered 10's across the board.