The al-Qaeda threat to the United States, while still real, no longer meets those standards. At most, al-Qaeda these days can mount sporadic, isolated attacks, carried out by autonomous or loosely affiliated cells. Some attacks may cause considerable loss of life, but they are nothing like the military operations that define an armed conflict under international law.
Obama himself has said that the core of al-Qaeda — the original enterprise now based, if anywhere, in the tribal areas of northwestern Pakistan — has been “decimated.” Its affiliates, such as al-Qaeda in the Arabian Peninsula and al-Qaeda in the Islamic Maghreb, are more robust armed groups but have limited capacity to project their violence beyond their regions.
These affiliates are significant actors in Yemen and northern Africa, but it is far from clear that they pose a threat to the United States greater than, for example, Mexican drug cartels or international organized-crime networks — organizations for which few would characterize U.S. containment efforts as “war.” That the United States continues to deploy military force against al-Qaeda is not enough to qualify that effort as an armed conflict, because if it were, a government could justify the summary killing of “combatants” simply by using its armed forces to do so.