If the body shape (outline) is the registered mark, then using that mark in the class of goods where it's registered is Trademark Counterfeiting.
That's the foundation of the argument, and the source of the term "authentic".
Whether or not the courts side with Gibson on all of its registered marks remains to be seen.
Again, "likely to cause confusion, to cause the mistake, or to deceive." That manual doesn't address a situation where one product has two or more separate trademarks. Dean's headstock shape and brand name will never be confused with Gibson's trademarked headstock shape, brand name, and logo.
Gibson already tried this in their suit against JHS. They lost because JHS' guitars had a different headstock with a different brand name.
Nobody knows what will happen in court, but if Dean doesn't cave, I'm confident they'll win on appeal. I also think there's a good chance that a consortium of companies can get Gibson's body shape marks cancelled.