Well I finally noticed this sentence that answered my initial question:

"Only individuals owing capital gains tax are required to file a capital gains tax return, along with a copy of their federal tax return for the same taxable year. "

This page has a good description of the calculation if you click on the "File a capital gains tax return without access to the account" button towards the bottom of the page:

https://dor.wa.gov/manage-business/my-dor-help/capital-gains-my-dor-help