This part of Mormon's description of the functional organization of Alma's church is somewhat problematic in that he has previously noted Sabbath observance as a feature of the church (verse 23). We cannot tell from this verse whether the "one day in every week that was set apart that they should gather themselves together" was the Sabbath or another day. It is quite possible that it was a day in addition to the Sabbath.
In addition to the decreed day of assembly/teaching, they were also "as often as it was in their power, to assemble themselves together." Alma is creating social structures that emphasize both the community and the religious foundation of the community. Rather than the social segregation of Noah's reign, Alma is fostering a sharing group, one that sees themselves as equals, rather than one that sees hierarchies of social status. The social division is only one of teacher/student. There is expressly no distinction of economic-producer/consumer. In fact, it is quite the opposite, as Mormon describes below.