There are many reasons. I got four types of reasons. Some of them could be applied to any other game, but this game sort of "transformed" them. You'll understand. It's from the least important to most.
1. It's Naughty Dog. Now i'm not any fan girl and i usually tend to respect and admire the work, and not the people who do it. BUT what is transformed in this game as opposed to others, is the fact that i played nearly every game of the company, liking and loving most of them, so i have grown to expect good things from ND, wait not good, but great, because i saw that with every new game they get better and challenge themselves.
2. It's a post-apocalyptic game and third person stealth, shooter etc. It could be any other game. BUT what is transformed in this game as opposed to others for the post-apocalyptic part:
the environments are beautiful, realistic, reflect the the loss, the end of humanity, the beauty of how things were and how they ended up, the sad feeling of something long gone. Combine it with the title "The Last of Us" and you just know this game is much deeper than just shooting and full pump action, you just know it's more "realistic" and literal.
As for the third person shooter, stelth, survival game etc, the thing transformed is the incredible enemy AI, which makes you feel like this could happen in reality, as if they have a brain and tactics and respond to everything you do in the game. Also it's not just running and gunning, you have to think your way through, you have limited supplies and just honestly, it's fun to punch
to run away to hide.
You know why? Because it feels realistic, fu*king finally we have that in a game, meaning you get more immersed.
3. The fact that it is story and character driven. BUT what is transformed in this game as opposed to others, is the fact that they say it is character driven and it really is character driven. No horrible voice acting, no unrealistic ideas and action, no gameplay that has a big contrast with the cutscenes (the last one is obvious in Uncharted, where in the cutscenes you feel human and real, and the charactes are just grounded, flawed like all of us and, i'll say it again, human, but the gameplay has contrast cause suddently you are jumping from collapsed buildings, running and gunning everyone, killing so many without a scratch on you, surving things you may not survived in real life). Aside from that I'm all into deeper emotions, meanings, no cliches, refreshing ideas. The sort of things that challenge you as a person and make you think of yourself, the person you are, the world around you, that make you think about morals, love, death, pain. Usually i read books to get that feeling or watch movies. Nobody expects that from a video game because stupidly there's an idea that video games are supposed to be just games for fun and for fifteen year old boys to enjoy, or just not mature enough to be realistic. But things started changing with Heavy Rain, Bioshock, Uncharted and other games which don't pop into my head right now. The Last of Us proved that video games can actually be mature, realistic, satisfying, and have even a stronger impact on you than movies and books. Why? Because movies you just watch. With video games you control what you watch. Because with books there is no sad music, not voices, no visual, with video games there's everything! Because with video games you have the ability to have extra background story with side quests, or in the case of TLOU conversations, artifacts and exploration, you have the ability to explore the world you are in, and importantly you have a choice for more, or different. So TLOF proved that we can have a story and character driven experience so much easier than other entertainment source.
Say what you want, the moment i saw Ellie i knew that ALL the above reasons were gonna be true. BUT what is transformed in this game as opposed to others, well there might be nothing transformed cause i can't think of any other game that introduced such a character, but if it transforms something, is the fact that she is a little girl, cool, too important for the plot of the game, brave, a mysterious kid that was actually born in this post-apocalyptic world, curious about the world before the infected, a kid that swears a LOT, and is beyond her age. A kid that, from everything we saw, was going to be the center of the game, and even maybe the most important character or even the protagonist, if everything evolves around her. We don't see that in games, and that gives a different feeling to the game and pushes our curiosity as to "why is there a kid protagonist which appers in front of the box cover of the disc and seems so important?"
That thought makes it obvious that reason 1 - ND has something special for us yet again, reason 2 - this post-apocalyptic game is gonna play and feel different from others with a little girl mysteriously pushing the plot, reason 3 - you know there's gonna be something "human", character driven, emotional when there's a girl like Ellie in it. So Reason 4 hugs all the other reasons and transforms them, subconsiously into something that no other game has achieved yet.
Sorry for the long post but, i'm not lying when i say that i really though of all of these before buying the game. Watching videos, hearing the features of the game and searching thoroughly what it's about, subconsiously made me think of all of these. But the truth is i got more than i ever expected and i could not believe it how little all of the above seemed in comparison with how much the game stood to the expectations and a gave us lot more!
So...what about you? What reasons did you have to buy the game?