Yes, retail sales tax applies on fishing charters that begin and end in the state of Washington. It does not matter that the actual fishing may occur outside of Washington waters.
Starting October 1: Some business services are now subject to retail sales tax, as required by state law, ESSB 5814. When you buy these services, vendors should add sales tax to your bill. If you sell these services, you should begin collecting retail sales tax. Learn more about Services newly subject to retail sales tax.