Here is a link to the treaty. Read it yourselves. Don't rely on people with an agenda to tell you what to think.
After a cursory check, the above two sections tell me that gun nuts in the US don't have anything to worry about.
RECOGNIZING that states have developed different cultural and historical uses for firearms, and that the purpose of enhancing international cooperation to eradicate illicit transnational trafficking in firearms is not intended to discourage or diminish lawful leisure or recreational activities such as travel or tourism for sport shooting, hunting, and other forms of lawful ownership and use recognized by the States Parties;
RECALLING that States Parties have their respective domestic laws and regulations in the areas of firearms, ammunition, explosives, and other related materials, and recognizing that this Convention does not commit States Parties to enact legislation or regulations pertaining to firearms ownership, possession, or trade of a wholly domestic character, and recognizing that States Parties will apply their respective laws and regulations in a manner consistent with this Convention;
Article I
Definitions
For the purposes of this Convention, the following definitions shall apply:
1. "Illicit manufacturing": the manufacture or assembly of firearms, ammunition, explosives, and other related materials:
a. from components or parts illicitly trafficked; or
b. without a license from a competent governmental authority of the State Party where the manufacture or assembly takes place; or
c. without marking the firearms that require marking at the time of manufacturing.
After a cursory check, the above two sections tell me that gun nuts in the US don't have anything to worry about.