In more recent history, Hindu gods have often been identified with the god Vishnu. Rama was an avatar of Vishnu, therefore he remains an example of Vishnu manifested as a king.
As early as the Ṛg Veda, Indra is likened to a king among gods, hence a model of Aryan warrior kingship.
In the Manu Smṛti, kings are said to embody divine particles from all the gods, therefore they are have greater inner power than ordinary people.