They are for non-US citizens who act contrary or independently to the policies of a specific foreign country.
As a US citizen, the legal method to execute Al-Awlaki would have been to; charge him, capture him, try him, convict him, exhaust his appeals, and finally execute him (assuming that there was enough evidence to do that).
This now antiquainted process was formally known as "trial-by-jury" in a system of justice which enforced separation of powers to prevent the possible re-emergence of the absolute tyranny of a king.
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