The seller and/or buyer likely don't need to be FFl's,,I'd guess that the 'new law' is simply the 'All (private party) sales must go thru an FFL so that a NICS check is done on the buyer' routine.
Something that has become quite common around the country thru State by State legislation.
On a Federal level..It was (still is?) House Bill HR8 and it constantly being rallied for by the anti-2A groups as the needed legislation to end all that is bad on the planet.

Third Party Transfers the FFL's call them, and they make a buck on them and never have the gun in inventory. Just charge for the BG check and paperwork.
Some don't do the 3rd party xfers at all, they don't have to if they choose not to under the Fed FFL regs.

If every transfer required that the buyer and the seller be an FFL, there would be no more GunShow. Just a gathering of Dealer FFL's.
On second thought, maybe that's a step in the right direction if you're thinking like an anti 2A person.