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In a word, no. That EO, and the whole series it's part of, don't restrict the DOD. They restrict the intelligence community. Nothing stops the military from targeting a head of state - or literally anyone else - if they are declared a legal target / combatant. Not sure where this whole "the military can't kill certain people" idea has come from. Probably news organizations like CNN, NBC, ABC, et al who just clip one-liners from EOs and use them to promote narratives which support their own motives.

Additionally, I would assume that Trump was advised and approved of the targeting. I don't see how one President could unilaterally limit another President with an EO given they hold the same office.

When the Italians give us military advice, we'd better listen. I mean its not like they've lost every war they've ever fought in the last 1500+ years.... oh wait, they have.