Maybe it includes a reference to citizenship but it does not define it as a constitutional concept. It also certainly doesn't make it a requirement of the constitution, as sitting US politicians or the OP are currently arguing.
If this is what you are defending than we couldn't disagree more.
It doesn't define a lot of things; treason's the only crime defined, for example, but we knew a whole bunch of others existed on day one.
It does clearly imply a difference between "natural-born" citizens and naturalized ones, and that citizens and residents/people/persons aren't the exact same thing.
The choice to use "citizen" in some spots and "person" in many others seems very deliberate.
Then we agree; it very much includes the concept of citizenship.