http://library.municode.com/index.aspx?clientid=16607
You click on Title 9, then Chapter 3. I actually cannot discern where the applicable statue can be found. I guess the city is saying the couple are running a church outside of the area zoned for that purpose. I cannot find the exact verbiage as stated in the article.
It certainly appears that (perhaps) overzealous bureaucrat(s) is/are misinterpreting the Ordinance since the table also lists the following under "Notes and Exceptions": Includes churches, temples, synagogues, monasteries, religious retreats, and other places of religious worship and other fraternal and community service organizations.
It certainly appears that the intent of thios part of the Ordinance is to empower the City to have some zoning control over where, how and how many Churches, Moose Lodges, VFW Halls, etc., are constructed in residential areas.
In my opinion, a privately held Bible study, held in a private home, regardless of its size, would not fall under this part of this ordinance (although other portions of the Ordinance may, indeed, restrict how many cars can park on residential lots, etc.). Depending upon the behavior of, and decisions taken by, the government officials of the city during the couple's appeal, this COULD remain a simple Zoning/"Use"-definition issue, instead of turning in to some kind of 1st Amendment fight.