Is there a gun show loophole?

No. This is a deliberate misconception, pushed primarily by groups such as the Brady Campaign, Everytown For Gun Safety, etc. The same laws which apply to buying a firearm anywhere else apply exactly the same at a gun show. A licensed dealer must do the NICS background check, just like if they were selling it at their own shop. In a state which allows a seller to privately sell a firearm as personal property, it can be done at a gun show just like anywhere else. If a state requires universal background checks for firearms transactions, that is likewise every bit as applicable at a gun show. The 'unlicensed dealers' these groups like to cite so much - not everyone who sets up at a gun show is selling guns. You'll also see tables set up to sell militaria and other memorabilia, non-firearm hunting and camping supplies, and a range of other products which are not firearms. Those sellers do not need a license to sell firearms, as they are not firearms dealers.