In my opinion, the wording is, at best, ambiguous:
U.S. Citizens on closed-loop cruises will be able to enter or depart the country on the cruise with proof of citizenship, such as an original or copy of his or her birth certificate (issued by the Vital Records Department in the state where he or she was born) and, if 16 or older, a government issued photo ID.
It's not real clear whether the original must be issued and a copy of that is fine. OR if both the original and copy must be issued by the Vital Records Department).
Since what you get from the Vital Records Department is not the actual original birth certificate (at least where I live), what's issued is a "certified copy of the original" document. And, thus, is a copy issued by the Vital Records Department.
All that being said, there are reports of people just using a xeroxed copy of the copy they got from the Vital Records Department to board cruise ships.