Even if he doesn't do the hands-on design work himself, he's clearly good at both recognising engineering talent and evaluating information that's presented to him. You couldn't have either of these skills without some engineering knowledge.
But what you described is just being a CTO. That's an important job, but is still separate from being chief engineer.
From that Reddit thread: https://www.reddit.com/r/SpaceXLounge/comments/k1e0ta/eviden...
Where would we be right now if [pick any inventor] had listened when the experts said, "it won't work"?
An inventor's job is to have a big imagination. A successful inventor usually has enough of an engineering background to test their hypothesis and refine as needed. Most of them also know how to gather highly educated minds to help them.
Many successful inventors do not have deep academic backgrounds, because often those educational backgrounds tell them only what is impossible, not what is possible.