While the author has mentioned his desire to leave certain aspects of the experience open to interpretation, a brief glimpse across a few forums on the game highlight a common public construction of narrative consistent with my own. I don't wish to divulge further for fear of hampering the experience and direction of anyone else.
What I am most impressed with in this game is the delivery; the purposefully simple style and structure of the interactivity. Combined with deliberate musical cues and accentuation, a story forms out of the most basic of game elements and ends with a (likely) unexpected meditation. There is a holistic series of events here, and it may only come together after another play-through or two, picking up the visual and audio clues that were originally overlooked.
Of course, you might just whizz through it and apathetically wonder what I'm carrying on about.