Jon Snow will be King in the end

The same could be said of Daenerys, Sansa or Tyrion.

GRRM has never made a major character of any of the kings. Robert, Stannis, Renly, Robb, none of them ever had their own chapters.
Cersei has chapters in the last two books but her taking the throne could be a show-only thing, which would make it a severe but not altogether surprising departure. So a speculation could be offered that none of these characters will ever take the throne in the books and that the show would not change that outcome unless the throne no longer really matters at the end. 

Maybe the bittersweet ending is that none of the "heroes" wins and gets the silly chair. Maybe they sort of come to accept whomever happens to sit there once the dust settles. No big triumph of the "good guys", just plain boring reality. Maybe Tommen lives through and turns the Red Keep into a kitten farm or Sweetrobin somehow gets there and does marry Sansa after all 

They said it won't.
But it could.

Still, I don't think the "game of thrones" is the relevant thing in the end. It's not a horse race.
Lord of the Rings was not about Aragorn becoming king and I think that same logic will apply here, especially after GRRM told of his admiration for "The Scouring of the Shire" chapter and used it to explain his intent of a bittersweet ending.

I also think the show will not make anyone appear as a clear winner.

I think there are three protagonists. Add Tyrion to these two. I wrote about this long ago in my thread about taking sides.
He's been sidelined in later seasons but remains a big favourite and his role as the wavering adviser between Daenerys and Jon confirms this. They form the "good trio" and having one of them take precedence is a bit of a blunder from the authors' point of view. That division they've created in their audience may not turn into a disappointment for two thirds of it.

I believe the way the show will come out on top of this is by taking no side and having them all three fail, fall or retire. I can see them all three die. I can see Jon declining a ruling position and either being content ruling the North or even abdicating in Sansa's favour. The latter was foreshadowed in S6E10, when he told her she is the Lady of Winterfell. Jon does not feel like being the leader of anything, he was always made to be by others.

There also have been reasons to suspect that the Night King didn't want Jon dead. The fight with the White Walker at Hardhome is the key to this. He could have killed Jon but only yanked and kicked him, then parried his sword as if he wanted to take him alive.

I firmly believe, though, that the magical aspect is meant to recede by the end of the story. White Walkers and dragons will be gone again, ice and fire will form a puddle, resurrected Jon and unburnt Daenerys will be out of scope, leaving normal people to pick up the pieces. It could be Tyrion, Sansa, Cersei, all three of them or none of them. Maybe Davos will be president.