The point is a declaration of war and a state of war IS an anachronism to the point that summary execution during wartime isn't done because there is no war time anymore, there are extended military actions under the War Powers Resolution of 1973, usually, but not always, accompanied by a UN Security Council Resolution. So just like declaration of war is an anachronism, so is summary execution during wartime is an anachronism.
Trying to use a semantics argument against a legal framework argument by saying that semantics don't matter, except in the case where the semantics say you get to feel justified by ending another human beings life (a fellow American citizen, no less) is also completely irrational and held only by clueless, non-worldly people who can't muster the energy and attention span to actually understand consequences.