We do in fact have background checks, and have for a few years.
Without the "semantics" I can only assume the 37 states mentioned don't require then for intrastate transfers. Interstate transfers have to go through a federally licensed dealer, and that dealer has to file the proper forms and get the background check done.
https://www.fbi.gov/services/cjis/nics/about-nics
https://www.fbi.gov/services/cjis/nics