It’s not necessary for IC, why would it be necessary for management?

Management is only one part of a CTO's job. An effective CTO needs to have strong technical acumen, so that they know what to prioritize, who to empower, and how to effectively communicate with a wide variety of stakeholders and partners. In addition, they need to have credibility in the eyes of the technical teams they lead. This usually comes in the form of past technical accomplishments, but can also be fulfilled via strong credentials, depending on the organization. In the case of Pentagon, which is a very formal organization, credentials will be absolutely necessary, which is why I think this guy is going to be... not very effective at his job.