Reading the news reports on the bill, there doesn't seem to be any specifics. It appears that the bill would give the Washington Department of Commerce the ability to ban the sale of certain tires, but it doesn't say what criteria is to be used.
California has legislation that would ban any tire that on the average doesn't equal the OE tires. How that is to be done is unclear, but they have been working on it for quite some time and have reached an impasse - the legislation would effectively ban the sale of 99% of the currently available tires. The US Tire Manufacturers Association (USTMA) has been working with the California Energy Commission (CEC) on this. I don't think the CEC can propose anything that will work = the legislation has to be changed.
I go into more detail here:
Draft Framework of California's Replacement Tire Efficiency Program
I suspect the USTMA will be active on the Washington State legislation as well.