So basically Obama is out of compliance. He has made a calculation to ignore what the written rules say, because history is on his side. Unfortunately, as far as the law goes, that bet is almost certainly right.
Thus the Supreme Court’s solution to the problem here was to rely on Congressional authorization of war as a sufficient substitute for Congressional declaration of war. The Court never directly addressed the ship-owner’s point that the Constitution speaks only of declarations of war, not of authorizations. The Framers would have been spinning in their graves.