FEDERAL law requires FEDERAL Firearms Licensees (FFL's) to follow all FEDERAL laws and guidelines, regardless of the location.
Prior to the Gun Control Act of 1968, FFL's were prohibited from doing business at any place other than the address listed on their license. This changed in 1986 with the passage of the Firearms Owners Protection Act.
Private party sales (no FFL involved) are governed by state and local laws and codes, regardless of the location.
There is no "loophole" specific to gun shows. Period. End of story. The gun show loophole term was created as a political lightning rod following two ATF studies that suggested that gun shows were the #2 source of illegally purchased firearms (following straw purchasers which the ATF rarely prosecute). Interestingly, straw purchasers were also a large part of the illegal transfer of firearms sold at gun shows.
So, if the ATF would simply prosecute and jail straw purchasers under existing laws, gun shows would be a non-issue. Instead, the ATF allows straw purchasers to make illegal purchases and transfer the firearms across international boundaries, loses track of said firearms and does nothing when said firearms are used by Mexican drug cartels to kill U.S. citizens.
FWIW, 0.8% (less than 1%) of prison inmates report obtaining their illegal firearms at gun shows. Repeat offenders are even less likely to do so than first time offenders.
The so-called gun show loophole is nothing more than a false flag created by anti-2A liars for political purposes.