Appreciating Dear Esther requires that you leave all your expectations about games at the door. You don't so much win as you complete the story, turn the final page. If games are meant to have high scores, enemies or goals, then Dear Esther might not be a game. Then again, the answer might not be so simple...
In Dear Esther, you receive disorganized snippets from a letter, or several letters. You're left to piece the narrator's purpose together, the island's place in the story. This does certainly qualify as an objective, even if it's lacking in a traditionally defined way to achieve it. You have to listen and take everything in. You have to do your own thinking. If thinking isn't part of the underlying mechanics of any game and if thinking *cannot* become a game mechanic in and out of itself, then I'd say we have a problem.
I personally consider the player's own journey to be a mechanic in and out of itself. Considering this, a surface analysis would make it clear that this isn't a game, while going a little deeper does reveal that Dear Esther has enough gaming conventions to potentially be worthy of the title.
You won't earn Achievements, here. The name of the game is allowing yourself to experience something, which is the most informal achievement of all, what all games should strive for. You won't solve puzzles; except what's given for you to mull over. You won't defeat anything other than the plot's initial opaque nature. This feels like a game to me, albeit one where the controls are less WASD and my mouse as they are my mind and my ability to receive what's being given to me on an intellectual and emotional level.
As a game, Dear Esther is treading brave new grounds. As an interactive art piece, it has a comforting familiarity that's usually lacking in other examples of that genre, such as Oddyseus 101 - an interactive reading of a segment of James Joyce's version of Oddyseus. The artiness in that piece is obvious, but there's no sense of familiarity, no recognizable medium to give the experience a comfortable fit. Dear Esther doesn't have that problem.
As a narration or a story, it absolutely works. The visuals complement the narration perfectly, and what could very well be a ghost story ends up being draped in a delicate mixture of brooding thought and little snippets of Gothic anguish. This is something Poe would be proud of.
That's also where the problem is located. We're used to clear and recognizable divisions between forms of communication - books sticking with books and games with games, Art with Art. Things are changing, and this is why some people cling to previous definitions of artistry (i.e. Roger Ebert) and why others think this couldn't conceivably be a game.
The real question is: Does it *need* to be a game? Does it *need* to be Art? Can't it simply *be*, there to be taken in for what it is and what it has to offer?