The preamble is who authored the constitution
Article 1 is all about how congress works
Article 2 about the president
Aritcle 3 about the courts
Article 4 about the states
Article 5 about the constitution
Article 6 about which laws are important
The Bill of rights further limits the power of government
Nothing specifically is about the people. The clause you state limits the powers of the state to take rights away from people.
The Constitution does not grant rights to people - because people (all people, globally) have all the rights by default. It does grant rights to government to do certain things, and it specifically limits the power of government to take away rights from people.
All the constitution has to say on firearm ownership is
> A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
No mention of citizens.
The constitution does mention citizens
1) Limiting people from congress/senate/president unless they have been citizens for various lengths of time
2) The supreme court applies
3) States can't discriminate between people from one state or another