The term, 'first to every loose puck' doesn't do it justice because that implies there would be some sort of race. There rarely was with Gretzky. He was usually already there.
Hah! After reading your use of the phrase "first to every loose puck" I stopped reading, got all excited, and was going to back up your point with the argument that Gretzky didn't chase pucks, pucks chased him. Then I read the rest of your statement and saw you made exactly that point. So, ummm . . . "ditto!"
That really is a great video to show those who don't understand how Gretzky was so effective. Even past his prime, it shows you his 1) crazy good anticipation, 2) ability to outmaneuver one of the fastest players in the game, and 3) incredible shot accuracy against an all-time great, and modern era, goalie. It's often very hard to pick any of those things out from a random Gretzky highlight, but all three really jump out at you in that clip.