Look at the best games of this year (or any year). Look at how almost all of them are about saving the world or some other giant conflict. Gone Home is a human story. It's completely inconsequential to everyone else in the world. But to the characters of the game, it's the most important conflict in the world. There are NEVER games like that. That's why it's special.
This. I would be pretty hard pressed to think of a single other story driven game that didn't involve some sort of massive conflict usually in some sort of fantastical environment. Even something like To The Moon still had a sci-fi bend. I think one of the key issues with gaming among the general populace is that the types of stories games tell are all very similar. They are summer blockbuster type stories, maybe not in scope, but in style. There has never been, to my knowledge, a game equivalent to something like American Beauty. Many of the best movies don't see the world in danger. Many don't see anyone in danger. Many just involve the lives of everyday people and the things they deal with. Now Gone Home is not the greatest story ever told, but it is the only story of this type ever told in a game. It paves the way for similar games to tell better stories.
As far as this specific story and the way it is told, I think the best part about it is how it plays with your expectations. At the beginning of the game you expect something terrible to have happened. You hear Lonnie's messages on the answering machine and expect that she is in danger, not in the throes of young love. You expect the red liquid in the bathtub to be blood not hair dye. You expect the basement to contain the ghost of year's past and the attic to contain the dead body of your sister. You expect the parents to divorce, the father to fail at getting another book published, the mother to have an affair. But in the end none of those things happen. By playing with tone and player expectations, Gone Home manages to keep things unexpected. You keep expecting things to go terribly wrong but they never do. And that is true of both gameplay and story. It's a merger of gameplay and narrative that defines the best interactive stories. Nothing bad happens in the gameplay of Gone Home. There are no monsters, no ghost, nothing. You expect the gameplay to go in a certain direction based on the setting and the tone, just like you expect the story to go in a similar direction. It is in fact the exact opposite of ludo-narrative dissonance. It is one of the few games to achieve true ludo-narrative harmony.
EDIT: Also, @roadshell, I noticed you used the term cognitive dissonance to describe this game, but cognitive dissonance is a mental issue where a person believes one thing but does the exact opposite. I think you meant ludo-narrative dissonance, which describes when the gameplay of a game is incongruent with the story it is trying to tell. Maybe the best example of ludo-narrative dissonance is the Uncharted series where Nathan Drake is presented as this nice, likeable guy in the cutscenes but in the gameplay he ruthlessly murders hundreds of people without a shred of remorse. Nothing in Gone Home in any way presents ludo-narrative dissonance. Contrivance? Yes. But contrivance occurs in everything from books to movies, and this game was at least a bit more believable than your standard audio logs.