The "son of Atreus, king of men" is Agamemnon.  He is the king of Mycenae, and his brother Menelaus is the king of Sparta.  (Both Mycenae and Sparta are Greek city-states, small kingdoms centered on a city.)  Agamemnon is the leader of the Greek army, but many of the Greek heroes (like Achilles) are themselves kings or the sons of kings, with their own followers fighting as part of the Greek army.  Although Agamemnon is their leader, they are not subordinates whose power comes from him.

Notice that Agamemnon and Menelaus can both be called "sons of Atreus" for their father, Atreus.  Menelaus is the legal husband of Helen, whose elopement with the Trojan prince Paris is the cause of this war.