[WARNING: The below post contains some small spoilers.]
Braid is a very strange game. I just finished it and I'm not sure what I feel. I wasn't expecting something so... lyrical, maybe? I don't know what the right word is. Braid is one part poetry, two parts hard-core puzzle game. I'm not sure how seriously the metaphorical layer is meant to be taken. On one hand the poetic bits feel very "separate" from the game. You can simply ignore all the text if you want. Yet the graphics, the lovely Van Gogh-like art style, is a bit harder to ignore. The music also does much to create an introspective, dream-like mood. Even without the text, it's difficult to take Braid simply as entertainment.
The big mystery of the game, I suppose, is what the gameplay has to do with the story. There clearly is a connection, but it seems deliberately obscure. On the most basic level, Braid's traditional platforming elements and time manipulation stuff seems intended as a loose metaphor for the trials, mistakes, and corrections in a relationship. The "princess" of this game seems like some weird ideal of romantic love that the protagonist is forever in search of. Or maybe she's a metaphor for failed relationships? I have no idea really. Whatever the case, it is clear that she is a metaphor, which, at least, is something Braid seems determined not to let the player walk away from the game without realizing.
I haven't put much thought into interpreting Braid. I finished it after several hours of play, and my immediate impression is one of dreamy confusion. I confess to reading most of the text quickly, without really trying to find a coherent thread in it. I'm not sure if there is one, or if the text bits are meant to be disjointed fragments. The only reoccurring theme is the princess. This is probably why the final sequence, where you finally find the princess, gave me an emotional reaction. I couldn't believe I got so close to her, and even cooperated with her, only to have time rewind, and have her disappear like a phantom. Did I do that on purpose? Why was rewinding the only thing I could do? I wanted to be with her, if only to get some answers to all these bizarre feelings and images. But she just vanished.
Braid makes the most sense if you conclude that everything in it represents a dreamer's waking life filtered through a host of subconscious symbols. It feels like the dream of a gamer, an expression of the collective unconscious generated by a life-time of game playing. This, to me, explains all the references to other videogames, which are all videogames with princesses. Braid may be an attempt by a gamer to make a game that expresses the connection between frivolous game conventions and real life, of how silly ideas like "save the princess" seep into our consciousness and become part of our shared cultural experience. It may be an attempt to reform that silliness, by giving these ideas metaphorical value they normally lack. Braid could be seen as a critique of games like Mario in this way, where "saving the princess" is just some meaningless goal. Here it is meaningless as well, but its phantom nature has been twisted into a meditation on the elusiveness of happiness. The design goal of Braid, in essence, seems to be to reformulate the words "I'm sorry, but the princess is in another castle" as an existential crisis. So that when the dinosaur eventually asks you "This princess... does she even exist?" you honestly don't know. Even at the end, when you find her, she may still just be a phantom... one that you are forever chasing.