Quick read of the ordinance and I think you're reading it correctly. Also remember that the state law preempts handguns under the concealed carry law:
(430 ILCS 66/90)
Sec. 90. Preemption. The regulation, licensing, possession, registration, and transportation of handguns and ammunition for handguns by licensees are exclusive powers and functions of the State. Any ordinance or regulation, or portion thereof, enacted on or before the effective date of this Act that purports to impose regulations or restrictions on licensees or handguns and ammunition for handguns in a manner inconsistent with this Act shall be invalid in its application to licensees under this Act on the effective date of this Act. This Section is a denial and limitation of home rule powers and functions under subsection (h) of Section 6 of Article VII of the Illinois Constitution.
(Source: P.A. 98-63, eff. 7-9-13.)