It's limited to citizens because the Second Amendment refers to "the right of the People to keep and bear", meaning the body of citizenry. No alien has the "right" to own a firearm in the U.S.
The NBC TV show West Wing, in reruns on the local ABC affiliate (shows from a couple of years ago) slimed Texas's concealed-carry laws with an episode in which someone stood up in a Texas church and opened fire, whereupon someone else with a CCW license also stood up and opened fire at the bad guy -- but missed and killed a 9-year-old girl (Democratic pity party: someone has to die!).
It hasn't happened, but Worst Wing's writers had a high old time putting President Bartlett up on his high horse, slapping down his Texan VP on the subject. It's the gun-grabbers' dream scenario: "more harm to let them carry". Mind you, the scenario was identical to the Charles Hennard and Larry Ashcroft shootings in Texas; Suzanna Gratia Hupp was testifying about the Hennard incident in Killeen. Larry Ashcroft, whose name usually doesn't escape my keyboard or my lips, was a Phineas Priest, a kind of right-wing assassin, who went after the Baptists because the Southern Baptist Convention had "compromised" its segregationist theology of 50 years ago. He shot up a Sunday-school meeting, then killed himself with a curse on his lips.
That's not how the Supreme Court has interpreted "The People" with respect to other articles of the Bill of Rights, particularly the fourth amendment. From Findlaw
''refers to a class of persons who are part of a national community or who have otherwise developed sufficient connection with [the United States] to be considered part of that community.'' The Fourth Amendment therefore does not apply to the search and seizure by United States agents of property that is owned by a nonresident alien and located in a foreign country. The community of protected people includes U.S. citizens who go abroad, and aliens who have voluntarily entered U.S. territory and developed substantial connections with this country.
Thus it also includes at minimun, legal aliens. The case from which the quote comes is United States v. Verdugo-Urquidez, 494 U.S. 259, 265 (1990).