Does my wife need a no-fee passport to travel to Guam on orders since it’s a US territory and she already has a civilian passport as well?

She shouldn't need a passport to fly to Guam from any US Airport as long as it is direct. However, if she has a passport, she would be covered if one was needed.

Don't over think it. A "no fee passport" isn't a special passport or a passport category to itself. It's just a program used to produce passports to folks at no cost due to special circumstances such as Federal employment. There are three types of passport. Tourist (blue), official (dark red/brown), and Diplomatic (black). If she already has a tourist passport there isn't a reason to get another tourist passport.

If your spouse needs a no fee passport it will be written in your orders that specifically list her name, granting command sponsorship. For instance, Italy will state you need a no-fee passport and a Visa, Germany and Japan, just a no fee passport