RCW 9.41.100
Dealer licensing and registration required.
(b) A dealer may conduct business temporarily at a location other than the building designated in the license, if the temporary location is within Washington state and is the location of a gun show sponsored by a national, state, or local organization, or an affiliate of any such organization, devoted to the collection, competitive use, or other sporting use of firearms in the community. Nothing in this subsection (6)(b) authorizes a dealer to conduct business in or from a motorized or towed vehicle.
In conducting business temporarily at a location other than the building designated in the license, the dealer shall comply with all other requirements imposed on dealers by RCW 9.41.090, 9.41.100, and 9.41.110. The license of a dealer who fails to comply with the requirements of RCW 9.41.080 and 9.41.090 and subsection (8) of this section while conducting business at a temporary location shall be revoked, and the dealer shall be permanently ineligible for a dealer's license.
The above sections of the RCW dictate how a dealer conducts business at a gun show. Same as in their place for business.
As you can see dealers are required to conduct a background check on every purchaser including when they sell a gun at a gun show. A private seller is not required to conduct a background check when selling a gun. However; try it, go to a gun show in Washington and try to buy a gun. You will find very quickly that you can not do so unless you are a member of the sponsoring organization. To become a member or renew a membership you must annually pass a background check. Without a membership badge every seller is required to turn you away and refer you to the membership desk to have your background check run. Whether this is state law or not is a mute point as it is practiced at Washington gun shows. It should not become a state law to restrict private sales of firearms in any way. The system works as it is. We must retain the right to purchase and dispose of our own property without the interference from the government.
Do you think you should have to transfer a car through a licensed dealer? After all there are more Vehicle related injuries and fatalities in this state every year than there are gun deaths or injuries in the entire country and yet there is no mandate to check the driving record of a potential vehicle purchaser let alone a mandate to force a private citizen to use a third party who will likely use every transfer they broker as a possible bait and switch with a simple suggestion that they check out all the vehicles on their own lot before finalizing their purchase.