Some people believe that there is a "human social contract" or "natural rights" or some variation thereof, but it's incorrect to say that the Constitution enshrines that concept. What the Constitution says is that the rights the colonists already possessed, by virtue of long-standing practice and their status as Englishmen, were not prejudiced by the new Constitution.
It's blatant historical revisionism to assert that a group of people who didn't believe that black people in America had any rights somehow believed in a concept of universal natural rights that we should apply to people in Yemen or Afghanistan.
The Constitution is fundamentally a product of "social contract" thinking. The preamble says:
"We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America."
When you see uses of "the people" in say the First Amendment, it's a clear reference to "the people of the United States" not "people everywhere." It's not necessarily limited to U.S. Citizens, but it is limited to people who have some nexus to the U.S., either through citizenship or presence on American soil.