Except it does. The way he lands/hits the move is the basic definition of different execution.
I don't get how this is even an argument. He grabs an opponent, he hits them with a DDT, and he does nothing different except that he lands on the ground face-first instead of on his back with only one of his opponents arms grabbed instead of both. How does this change the fact that the opponent himself is landing in the same exact manner? How does it change the fact that it does the same exact damage as Ambrose's does with no apparent difference in impact at all?
In what world is the enzugiri a finishing move?
In the same world where a neck-breaker, a spinning-neckbreaker, a big boot, a clothesline, a DDT (of any kind), a leg-drop, a running knee, a punch to the face, etc. are all plausible finishing maneuvers. In other words, the whacky, cartoonish fantasy-land of WWE. How is an enzugiri any less believable than any or all of those things? I can't remember the last person who used it as a finisher, but ADR at least used it as a signature move that he would use to put people down before slapping the cross-arm breaker on them. It was always sold as one of his more devastating moves.
One of the fun and cartoonish aspects of wrestling is that you can condition people to accept almost anything as a finisher if you use it as one long enough, and the enzugiri would at least be an original one if nothing else. I'm not even saying it's the best choice for a finisher, but it's a suggestion.