Thinking about this more and more, only Arya could have killed the Night King.
Sure, in an epic sword fight, Jon Snow may have got the job done, but for the same reason Yoda and Obi Wan couldn't face the Emperor in a rematch, Jon Snow couldn't be the one to take down the Night King. Why? Because just like we saw in the episode, he couldn't get to him.
The Night King saw Jon Snow coming, and raised more dead to stop him.
Of the people at the battle, ONLY Arya would have had the skills necessary to get to the Night King.
Could Jaqen have done this job? I believe he could have, but he wasn't there. Each of the people Arya spent time with could have done the deed, but it was a combination of everything that made Arya the only one at the battle to be able to succeed.
Syrio taught her bravery. To look at the God of Death and say, "not today." He taught her the swift movements that made her hard to hit. This enabled her to take out a lot of dead people, and helped her stay alive. Melisandre's words reminded her of her first teacher.
Ned Stark was the most honorable man she ever would know, and of course her father. He taught her right from wrong, and instilled the importance of family. Her love for her father and his horrible death fueled her desires for revenge, fuel that was lit harder from the other deaths of her family. It also was her motivation to return home and keep her humanity. That leap to kill the Night King was more than a leap to save the world--at least to Arya. She was protecting her younger brother above all else. Family.
The Hound taught her that sometimes you have to fight dirty and there are hard lessons in life.
And of course, Jaqen taught her the stealth skills, and arguably the ability to fight in the dark--probably where she perfected switching hands without looking. Maybe he knew her destiny too.
I think that at least in this universe, the Lord of Light is the true god, and he manipulated everything to get Arya to that spot.
Without those stealth skills, Arya doesn't get close to the Night King. Even with them, he caught her midair, showing how formidable his own skills were. But she had that one extra move, the ability to blindly switch hands and make one final thrust--a result of the years of training.
But here's my worry. Most GOT fans are beyond pumped over this story.
They are looking at what Arya did and smiling. Some of the reactions on Youtube are insane. Arya Stark may be more popular than Tony Stark right now, and that's saying a lot.
But there are 3 episodes left. If Arya's purpose was to kill the Night King, where does she go from here? Cersei does have green eyes, and technically, that means Arya still has to kill her. But Melisandre has been wrong before. I can almost see a similar leap as with the Night King, only to see Arya killed by the Hound setting off the Clegane Bowl.
I hope not. GOT fans are on a massive high right now, due to Arya. If she doesn't survive the next 3 episodes, I think a lot of fans will be gutted.