Can rules rule (as in govern)?

Yes, they can, especially if the speaker is suggesting that it is the rules that govern and not any specific person or people, as people--politicians, kings, whoever--come and go but the rules remain, steadfastly imposing themselves on the citizenry to such effect that they normatively conform.

By the way, that's an example of an antanaclassis. An antanaclassis is a rhetorical device in which a phrase or word is repeated, though the meaning changes in each case. It is the repetition of a similar word in a sentence with different meanings, or a word is repeated in two or more different senses.

https://literarydevices.net/antanaclasis/#targetText=Antanaclasis%20is%20a%20rhetorical%20device,two%20or%20more%20different%20senses.