Congress can and does delegate execution of the laws it passes to the executive branch, like the coining of money, which power was given to Congress in the very same section of the Constitution, Art. I Sec. 8, as the power to punish Offences agains the Law of Nations. The former is just 5 paragraphs before the latter. We are not detaining and trying known soldiers, we are detaining and trying people who may or may not be "terrorists"
This is no different than the case of the German sabotours from WW-II. The only way to know if they were sabatours was to try them, which we did, by Military Tribunal. Spies and sabatours (which is pretty much what terrorists are anyway) don't carry ID cards you know, at least not foreign military ones.
that should be 5 clauses. All of them are part of the one sentence starting: "Congress shall have the power..".