That clause doesn't sound like they mean "unlimited guns for all".
Using the context before the comma, the "people" clearly means polis, as in society, not as in the "every human with a pulse" way we use it today.
The word "person" is used twice in the BoR, both times referring to individuals. The other 3 uses of "people" clearly refer to the collective polis.
This distinction, as people not merely being a plural of person, is laid bare in the fourth amendment: "the right of the people to be secure in their persons", that only makes sense if "people" means the abstract composition.