There are several threads that pertain to this with very good explanations. The key work to all these discussions is "Commercial". Are you using the vehicle for a commercial use? If the answer is no, as Stumpjumper replied, you have a private vehicle and are not subject to the CDL requirements. If you need an official position, check with one of the Weights and Measurement, State Patrol Officials to explain this.
You will have a near heart attack when you go to license this vehicle if it is under 30 years old. Over 30 qualifies for an historic Vehicle plate in WA. Even then the license was around 300 plus tax, which you already paid to GL. And depending on how you pay tonnage, it may be a bit more.
If your MOS has you driving large trucks in the service, we are working on ways so that current service members can acquire their CDL's while in the service, so when they get out, they would be ready to transition into a career that a CDL is required. If you need that info, PM me and we will talk about it.
None of this is to blow off a CDL with a cavalier attitude. Be familiar and comfortable with your truck, if you aren't, have someone work with you and check you out on it before you take it on the road.