There's a few reasons why The Last Of Us has been so well received.
The acting and production values are excellent and it captures the tone of the videogame perfectly.
Also it's extremely faithful to the videogame (some scenes are actually shot for shot) This is no surprise as the writer of the show Neil Druckman also wrote the videogame. Playing the game is actually like playing an interactive movie as they made the story the most important part of the game.
Even though I knew what was going to happen to Joel's daughter having played the game it still got to me emotionally.
It's definitely so far the best TV/Movie adaptation of a videogame