I've been reading people's interpretations about the plot of "Braid", and most of them strike me as not so much wrong as overly literal, or just incomplete. Here's my take.
Insofar as anything is literally happening in the game, it's happening in the mind of "Tim", the protagonist. "The princess" is his idealized notion of a former lover who left him in anger after Tim commits a serious transgression (the specifics of which we never quite learn). "The monster" is the man she's with now. A large fellow with wild red hair, he appears in beastly caricature in the "Lair" levels, but shows a more literal (and quite human) countenance during the final level.
Tim deeply regrets the mistake that caused this woman to leave him, and fantasizes about getting her back. But his mistake is so grave, and the severance between them so complete, that the most he can do is concoct a cartoony saving-the-princess scenario based on the video games he played as a child. This grants him some relief, letting him pretend that she left because a horrible monster kidnapped her, and not due to anything he did - even though he is entirely aware of the truth (it's in the very first passage of story-prose you find). He mixes this with a fervent wish that he could just turn back time and undo his error, and thus you have the style of the game's levels.
The game's final level is also Tim's final reconciliation of the situation. The first half of the level agrees with Tim's fantasies - the princess breaks free of the monster and cries out for help. Here comes Tim to the rescue! Touchingly, as he races against time to meet her at the end of the course, she matches pace with him, helping to remove the blocks in his path. But when he finally gets there, bang, she locks him out, leaving him with no recourse but to once again wish for a second chance. But when he runs in reverse-time though the same level, all the enemies that were threatening Tim have vanished. Now it appears that he the aggressor, with the princess frantically slamming shut all the doors between them as she flees. Back at the start again, as Tim looks on, she cries out for help, leaps into the open arms of the monster - who now looks like an armor-clad rescuer - and they sail off together. Tim then leaves the now quiet and empty stage, alone.
This is Tim finally admitting to himself the truth of the situation: there was no "kidnapping", and so there can be no rescue. The woman, his princess, left him of her own will, and there's no monster he can fight that will bring her back to him. My take on the epilogue level which follows is that here we have Tim wandering dejectedly through the ruins of his fantasy world, now unable to support itself under the weight of his new reality. Poor fellow.
At the very end, he finally re-emerges into the city night. He has lost the princess, but he's grown enough now to know why. And that's the end of that story.