The rook can do a move called castling, which moves both king and rook around should they not have moved during the game and the spaces between are clear. This is typically seen as moving the king into a spot of protection, but I suppose it could also be seen as moving the crown into a favored position, which can lend itself to a darker interpretation of what the move implies.

But if I had to guess, it is just a piece they chose from chess that doesn't imply anything they weren't going for. For example, if it was a pawn, then we would assume she is the one under manipulation, not the manipulator.

Except that the rook doesn't do that.