The Head of State in many monarchies are largely ceremonial figures. The validity of the regime depends more on the actual underlying government, whether autocratic, oligarchic, democratic or anarchic.
Even if Adam's heirs had dominion over the world, there is no law of Nature nor positive law of God that determines which is the right heir (to dominion over the world) in all cases between generations
“To confirm this natural right of regal power, we find in the decalogue, that the law which enjoins obedience to kings, is delivered ill the terms, Honour thy father; as if all power were originally in the father.”
The Decalogue also tells us to honor our mother ” And "why may I not add as well, that in the decalogue the law that enjoins obedience to queens, is delivered in the terms of “Honour thy mother,” as if all power were originally in the mother?"