Sure, but the whole Constitution begins with "We the People of the United States". You can argue that it should include non-citizens, but the constitution itself and subsequent applications are very clear that it does not. It is a somewhat odd proposition to claim the constitution of one country apply to all. Should the rest of the world have stopped drinking in 1919?
(Not a Republican mythmaker who loves torture, just stating the facts)
The purpose of the US Constitution is not to tell people what to do or not do, it is to define very precisely what the US Government can and can't do (and how it should function), and therefore it seems more than logical that it would talk about what the US Government can or can't do to people in general (or animals, or nature).
I don't know where you get the idea that the purpose of the Constitution is only about how the government functions. It is clearly the majority of the Constitution, but plenty of the Constitution is about what people (American citizens) can or cannot do. Constitution says you have to be eighteen to vote, you can't own slaves, and you can't sell booze from 1920-1933.
I think a lot of people are viewing the Constitution how they want it to be (a set of ideals about liberty and even then only the ideals they espouse) and not what it is (a legal document with centuries of practical use). You can say America is not being moral actors about how they are treating foreign people who don't live within its jurisdiction, but the Constitution has very little to do with this issue. To say it does is cherry picking what you like about the document without acknowledge the realities of it.
(Not a Republican mythmaker who loves torture, just stating the facts)