I'm not sure what "rule" means here because how I know of the word rule is as in soccer rules.
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Native speaker’s answer
Rebecca
Here, "rule" means to 'govern,' or 'control' or to 'be in charge of.' It's similar to how Kings and Queens used to be in charge of or "rule" countries and kingdoms. They were the ultimate governing power. Ex: The King's rule of the kingdom was short-lived because he died early. Ex: I rule this school. Everyone listens to me.