You are saying that there are people in Gitmo who were uniformed members of the Taliban, who fought following the rules of war. Or at least implied that. If those people are there, then yes the conventions apply to them. Personally I do not believe that any of the people there fit into that classification. If the President decides to extend convention rights to people who do not deserve it, well that's his perogative.

So if you can show me evidence that there are people who deserve convention protections there, I'll agree that they deserve it and admit I was wrong on saying that everyone in Gitmo doesn't deserve those protections. And that's deserve it as per the treaty, not what other people or organizations claim. But by and large I think it's a safe bet that the vast majority of people in Gitmo (over 90 percent) do not fall under the convention at all.