Games that classify as Art. This is one. Requires reading between the lines.
What makes the story so special is that as you progress through the worlds, you quickly realize that this story is not literal, but is metaphorical. There's something going on that makes the story yet another puzzle to solve. This is where the deeper side comes in. You cannot treat this story in a shallow manner, or you will not get it. It's like reading a short story by a poet, in which you have to draw out hidden but powerful meanings.
The ending.... is what will make your jaw drop with understanding. Besides the fact that it's utterly brutal that you have to acquire all the puzzle pieces to get there (i had to resort to the internet to get me through a lot of solutions, and i'm a pretty smart puzzle solver.....), both the written story, and the visual gameplay meet in a way that will blow your mind. You suddenly realize that something is terribly wrong with this. Things are completely backwards, both literally and metaphorically (time is completely reversed, despite the fact that you are pushing 'forward'). And the final confrontation will leave you speachless, as you suddenly experience why the last few levels have been like that.
The postlude will have story quotes that lead you in the direction of understanding what the metaphors were referring to. Once you beat it, you will be inclined to search over forums at what others have come up with to explain it, and it's very very awesome to just realize it all.
That's what makes it special. You are thrust into the realization of what you have done, just as the source of the metaphor and story had happen. This game is a work of art.