Ok, but that was not ordered by the president so is completely irrelevant to the discussion of presidential immunity.
Seems relevant to your lecture on military law.
It seems extremely relevant. Your argument suggests the president need only appoint a subordinate who will themselves give the desired illegal order without the president's public command. In the unlikely event the subordinate is called to account, the president can simply pardon them.
This is certainly not a hypothetical "parade of horribles", since Trump has already pardoned military officers convicted of war crimes.[1]
1. https://apnews.com/article/257e4b17a3c7476ea3007c0861fa97e8
President immunity as laid out by SCOTUS clearly covers pardons.
Including "I'll pardon you and everyone down the chain if you do a war crime" promises.