When King Pṛthu is described as an incarnation of Lord Viṣṇu, it should be understood that he is a śaktyāveśa-avatāra, part and parcel of Lord Viṣṇu, and is specifically empowered by Him. Any living being acting as the incarnation of Lord Viṣṇu is thus empowered by Lord Viṣṇu to preach the bhakti cult. Such a person can act like Lord Viṣṇu and defeat demons by arguments and preach the bhakti cult exactly according to the principles of śāstra.