Where did you read that this law, which authorized the Afghanistan war, was being used as legal justification by Obama for the strike on Awlaki?
The AUMF stipulates "That the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons."
It was determined by the Bush administration that al-Qaeda planned and committed the 9/11 attacks.
al-Alawki was a member of al-Qaeda and not just a member but a chief "officer" of al-Qaeda.
Therefore, under the AUMF, Obama is authorized to use all necessary force against al-Alawki. The AUMF does not specifically limit his use of force to foreign nationals.
I didn't read anywhere that Obama is using the AUMF as justification.