By virtue of his father being a British subject he would have dual-citizenship. As you recognized yourself the choice to retain U.S. citizenship exists making it self-evident that the person in question is only a U.S. citizen by naturalization. A “natural-born” citizen never has to make a choice or take any action to secure his citizenship status.
If that were true, then any country in the world could cancel out an American-born individual's natural-born status by granting them citizenship at birth. Lucky for us, this is not the case. U.S. law is the only thing that determines our status as American citizens, not decrees from foreign countries. This is why the U.S. doesn't officially recognize dual citizenship.