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.