First, you're wrong on the facts. The Gun Control Act of 1968 prohibited FFL dealers from selling at shows. That restriction was removed in 1986, under FOPA. But what we're talking about here is not FFL dealers.
The "gun show exemption" - good god, an angel on my shoulder is asking, why are you bothering - refers to two factual scenarios:
1) First, from the seller side, the law controlling who has to become an FFL dealer largely targets "do you have a storefront". This means that you can sell guns quite freely at gun shows without having to be (and keep records as, perform background checks as, et cetera) an FFL dealer. That setup imagines 'real dealers' as people with stores. But gun shows are now very large and very frequent events. You can, clearly, be very much in the gun dealing business - buying lots of guns from wholesale sources, selling lots of guns a week, doing it as your primary source of income - while operating only at gun shows and not having to register as an FFL dealer.
2) Second, from the buyer side, if you do your buying at gun shows you aren't "buying from your neighbor". Your experience is like that of going to a store; you have a huge selection, you can go practically anytime, and so on.
So, to summarize, the de facto gun show exemption is that in the drafting of the older laws regulating gun sales, legislators were presumably imagining "we won't apply normal regulation sales at gun shows, because we don't want to burden people engaged in piddly little private transactions with their personal property with the kind of rules we apply to dealers in stores." That's a pretty normal take in legislation generally - consider, for instance, the differences between how private party used car sales are regulated and how used car dealers are.
The massive growth in the size and frequency of gun shows, though, turned what was intended to be a pretty trivial loophole into a huge one. That's the 'exemption'.