It simply says that under the provisions of that Law, in the course of a covered person USING the provisions of THAT Law, no information about gun possession or ownership may be lawfully collected
EXAMPLE: No doctor or other medical service person treating a patient covered under the PACA ["Obamacare'] may lawfully ASK for or collect such information.
That PACA Amendment/section does NOT prempt the provisions of ANY OTHER laws covering firearms.
but, the Firearm Owners' Protection Act, Pub.L. 99-308, 100 Stat. 449, enacted May 19, 1986, codified at 18 U.S.C. § 921, does provide that the government may not maintain a national registry of firearms. I'm not certain about the details, but I do know there is a portion of this law that covers this.