It's just a very different video game.
For starters, it's not exactly a terribly 'fun' game. Not that it's not good or a great play, but that it's like Zero Dark Thirty, an incredibly well put together thing that's not easy to watch. Look at the Infected, the zombie-like creatures. Y'know what a couple differences are between zombies and Infected? Zombies are all men, and zombies don't scream and moan. Killing them is both terrifying and crushing.
As a game, it's exceptional. The thing is, it doesn't stop at being a game; The Last of Us is a narrative. Sure, graphics are exceptional (in an early scene you can see your reflection), but the graphics all serve the story. Gameplay; the item scarcity, the brutality of every kill, it all advances the feeling of the story. You're desperate: you've got a dozen bullets left between all your guns, one medkit, a molotov cocktail, and a brick. Gameplay is phenomenal.
But the way it intersects with the narrative is where it shines, and ultimately, horrifies. I found myself not wanting another fight, simply because fights were so violent and brutal. This isn't Army of Two or Assassin's Creed where you get a sort of glee out of slaughtering someone, every kill in The Last of Us is painful. Just when you're starting to think "yeah, I'm bad" you find yourself shooting someone right as he begins to plead for his life. Or you'll get swarmed and die. You're not playing a baddonkey, you're playing a heartless man with a singular goal. Gameplay has you doing things as Joel that you, as a player, would rather not do.
Again, it all comes down to the narrative. Neil Druckmann's script is exceptional. It's ruthless yet so full of emotion you WILL cry at least once. Character motivations are so clear and, in a page ripped from Game of Thrones, characters want something so bad they will stop at nothing to get it (once they know what it is). Moments between characters, especially between Joel and Ellie, build it up to where it's headed, to the ending. The game discards the usual pulpy fiction that accompanies games in favor of something that can only be described as literary.
The Last of Us is a beautiful, beautiful game. One that I'm still processing, much the same way I did with a certain episode of Game of Thrones or the ending of Chuck. It's such a finely woven piece of literature that leaves you in awe and emotionally drained. It dares to be a game that's not just 'fun' but deep and interesting too.
Also: It bears mentioning that The Last of Us doesn't have a morality system, there's no decision making. You're playing a story, you CANNOT opt out of doing some things as much as you want. YOU don't have a choice because YOU are Joel and you are doing what he would do. Joel is not you, you are Joel. Again: it serves the story.