He CANNOT change law with an EO only clarify. Current law exempts private sales specifically. He cannot change that.
21)The term “engaged in the business” means—
...
(C)as applied to a dealer in firearms, as defined in section 921(a)(11)(A), a person who devotes time, attention, and labor to dealing in firearms as a regular course of trade or business with the principal objective of livelihood and profit through the repetitive purchase and resale of firearms, but such term shall not include a person who makes occasional sales, exchanges, or purchases of firearms for the enhancement of a personal collection or for a hobby, or who sells all or part of his personal collection of firearms;
I hope this is true!