You cannot win any kind of MTT without luck. Heck, just look at the hit a 10 on the river for a straight
. He doesn't hit that, and he's out. He was behind from the getgo (AK vs. AQ) in that hand and was 9% heading into the river. But I am sure that every other player who made the final table (heck, I bet prbably every player who just made the money) has a similar tale of hitting a river card to win a hand.
The real question is not can you win a tourney based purely on luck (the answer would be no), but what is the percentage of luck vs. skill required to win? Look at some of the other hands on that video. McKeehan won a coin flip early when he had AK vs. QQ and rivered an ace. He won another big pot against Zvi Stern when McKeehen had a full house and Stern had nothing but bet into him any way (to me, that's another form of luck).
Is it luck to get AA? No, that's just poker. You play long enough and you'll get it. What is luck is when you get AA and somebody with AQ in front of you shoves all in and you scoop a big pot. That's the luck part.
Here is another example of luck for McKeehen (https://youtu.be/bMJ2qaxYQr8?t=16m25s). He gets pocket 6s and calls a pre-flop raise against some guy named Guan with QJ. McKeehen gets a 9-6-4 flop to give him a set. Guan check-raises the flop after McKeehen bets 550,000. Then the turn is another 6 to give McKeehen quads, and Guan bets 2.3 million on the turn! That's another example of luck is when your opponent picks a bad time to bluff against you.