No. He is demanding that state employees be vaccinated.
You are confused.
"Gov. Jay Inslee of Washington announced Monday that most state employees and all health care workers must be fully vaccinated against the coronavirus by Oct. 18, or risk losing their jobs."
...
"This would apply to both private and public sector workers, including 60,000 state employees, as well as 14,000 that work for King County and 10,000 employed by Seattle."