That is a fantastic video. It really highlights Payton's versatility and athleticism. This was a man who would do whatever you asked of him, and do just about all of it better than anyone else could.
People need to remember his toughness and strength as well, and this was not emphasized in this video. Payton was one of the pioneers of the "stiffarm," and many times he was able to gain an extra 2-5 yards by taking on hits instead of ducking out of bounds.
IMO, he was the perfect combination of power, elusiveness, speed, agility, and awareness that teams look for in a RB. All of this was evident when watching him play, but like another person said, he also has the stats to back it up. Brown and Sanders were great, great players, in fact second and third in my mind, but there is no other RB I'd rather build my team around than #34.
As for Rice, well, there is no other player who dominated his position as much as he did. You can certainly make an argument for him along those lines. He is to the WR position what Gretzky is to hockey players, lapping the field, so to speak. You might not like my argument, but I tend to give these RBs more credit due to the rapid burnout rate at the position.
And yes, you probably can tell, Payton was my (sports) hero growing up. It almost felt like losing family when he passed. So maybe you can't take my argument too seriously, considering my bias.