It surely isn´t a normal war. The definition of war doesn´t really match here, comparable to the legal status of the "war on drugs". This is terrorism, and terrorism is a criminal behaviour. That´s why the treatment of the inmates in Gitmo is so complicated: some are caught as Taliban right on the battlefield bearing their arms openly, while others were captured in non-war zones. You need to find better solutions "in the longer term", for the legal status of these people, that´s what Merkel thinks (and me too). Otherwise, it could be hard to consider your country a state that is based on what we in Europe call "Western values". I´ve heard even the Chinese put their inmates on trial...
As I noted before, the Geneva Convention avoids quibbling about such semantics in this matter by using the phrase "persons, having committed a belligerent act ".
Note the use of the term "PERSONS". In Article 5, the Geneva Convention does not limit itself to servicemembers of a state-sponsored armed force.
As far as "crimminal" is concerned, you can have "crimminal" behavior in anything from how you drive a car to how you treat a pet dog to how you "commit a belligerent act".
The language of Articles 4 and 5 of the Geneva Convention is clearly tailored to include individuals such as those belonging to al Qaeda.