The law is useless because there is no gun registry. LEOs have no idea who owns what gun or when they got it. Even going forward the background check is not tied to a specific gun.
There is no way to enforce this law, so next election they will be back with a desperately needed "fix", yep gun registration.
Are you talking about the same background (& registration) checks that I know about? That use form 4473 for transfers? Name, address, SSN, drivers license, plus make, model and serial number(s) of what is being transferred. They are very much tied to a specific gun.