Bruce,
The building code does not care what it is zoned as, it cares what it is built as.
If it is built as, being used as, a single family dwelling, then the IRC should apply.
But, if it is built as, being used as, something else ...
From the IBC.
- 1208.2 Minimum ceiling heights.
Occupiable spaces, habitable spaces and corridors shall have a ceiling height of not less than 7 feet 6 inches (2286 mm). Bathrooms, toilet rooms, kitchens, storage rooms and laundry rooms shall be permitted to have a ceiling height of not less than 7 feet (2134 mm).
From your photo, though, I suspect the IRC would apply.