It actually wasn't enacted by initiative 1639. It was enacted by the legislature because Washington's two-track pistol purchasing system was not compliant with the Brady background check requirements. You can find the implementing law here, along with bill reports, which go into the discussion of the FBI background check issue.
https://app.leg.wa.gov/billsummary?B...itiative=false
From the final bill report:
The FBI recently conducted a review of full POC and partial POC background check processing to determine whether states are processing background checks appropriately. In 2018 the FBI notified Washington that it is not serving as a partial POC on all required firearms transfers, including pistol transfers where the purchaser possess a CPL. The FBI indicated that the NICS Section will stop processing NICS background checks for these transfers, but has delayed this change until the state revises its laws governing these transfers, or June 30, 2019, whichever occurs first.
The legislature basically came up with a draconian solution to a problem that doesn't exist in other states, by requiring local L.E. to conduct background checks. The session law does require the state to come up with a single source point of contact system by 2022, or else the new law sunsets. I'm sure that won't happen.