The fact that she by chance happened to have the very same position during normal play gave it away. The probability would be astronomically low.

Not sure if you're referring to something else. But in the story she is just replaying the game that her grandfather played back in the 1800s. She didn't actually come up with that move from playing.

The coincidence isn't quite what you think it is.

In the story world, the puzzle probably took its precise form from that game. If the game hadn't happened, maybe Anderssen's unpublished notes would have included a similar puzzle, or maybe nothing along those lines. So the coincidence is "merely" that she's related to the person who played the game that begot the puzzle.

You ruined everything :-P