It seems to me, based on the history of what was taking placein 1949 and the post WW2 world, Art 3 clearly refers to civil wars and national liberation movements, like say what was happening in Greece, Italy, Yugoslavia etc...
Our current conflict is clearly of an international character. Further, the standard rule of construction is taht the President is entitled to complete deference in his interpretation of the treaty and the SC can't really question that.
Also, it's not entirely clear that the conflict even took place in the territory of one of the parties. Yes, Hamdan was in Afghanistan, but that territory belonged to the Taliban at the time, who weren't a high contracting party. The Taliban were not recognized as the legal govt of Afghanistan by the US so that is a point as well.