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If you were instead referring to this first sentence:
"Art 2. In addition to the provisions which shall be implemented in peace time, the present Convention shall apply to all cases of declared war or of any other armed conflict which may arise between two or more of the High Contracting Parties, even if the state of war is not recognized by one of them."
Then this sentence clearly only applies to conflicts that break out between High Contracting Parties (i.e. - signatories to the GCs), which may be to your point about al-Qaida not being a High Contracting Party.