So, are private firearm sales conducted at Gun Shows a loophole in that it bypasses the Background Check?
There is no "Gun Show Loophole".
If it's illegal for a person to purchase a gun, it's still illegal to purchase it at a gun show.
If it's illegal for a person to purchase a particular type of firearm, it's still illegal to purchase it at a gun show.
If it's legal to for a person to purchase a particular gun at a gun show it's also legal for that person to purchase it anywhere else.
There is
nothing you can do legally (with regards to gun purchases) at a gun show unless it is legal everywhere else.
If you are buying a gun from a private party at a gun show, exactly the same laws and legal restrictions apply at a gun show that would apply if you purchased it from that person in his home or yours, or on the street.
If you are buying a gun from a dealer at a gun show, exactly the same laws and legal restrictions apply at a gun show that would apply if you purchased it from that dealer in his home or yours, or on the street or in a storefront.
Don't know how to make it clearer than that.
There is no "Gun Show Loophole".
It sounds like you really wanted to start a thread asking the question:
"Should the existing laws be changed to require background checks on private firearm purchases at gun shows?" That's a different story altogether.