In the modern reading of this verse we have the affirmation of priesthood power by the authority of God. While this is a true principle, it is not all of what was happening in Alma's community.
In addition to the priesthood authority from God, these verses show how Alma organized his community to support righteousness rather than the potential unrighteousness of a kingship. Alma is a just man, and appoints in his "theocracy" other just men to be the teachers and priests. These men (we may easily presume them to be men given the cultural bias towards males that appears to have been part of Nephite culture) were appointed by Alma, not elected by the people. In this case, there is no democratic election process. We have righteous men appointed by righteous men.