It's still a private sale if it's not going through his books. It's just a private sale that has to go through a FFL. Some sellers in FL will require that their private sale in state has to go through a FFL. It's still a private sale, because the transaction is still conducted between two private parties.
Wayne, the same can happen here in Virginia. A private seller can insist on going through an FFL in his/her state to transfer a gun to a private buyer in his/her state. They tend to make that clear in the conditions of the sale right up front. I would still consider that a private sale too. However, you have to account for some variations here. For one, the seller/dealer is not in my state, so his transaction would not be considered a "private sale" in my state because we are not both private citizens of Virginia. Also, he didn't say he requires an FFL transfer in his private sale listing. I don't see any legal loopholes that work in his favor here.