The 14th Amendment does not mention Article II.
You are mistaken to believe that the 14th Amendment “further defined” Article II.
I’m relating what the court rulings have consistently been since 1868.
For example: Elk v Wilkins, 112 U. S. 94 (1884)
The distinction between citizenship by birth and citizenship by naturalization is clearly marked in the provisions of the Constitution, by which ‘no person, except a natural-born citizen, or a citizen of the United States at the time of the adoption of this constitution, shall be eligible to the office of president;’ and ‘the congress shall have power to establish an uniform rule of naturalization.’Const. art. 2, § 1; art. 1, § 8.
“This section [of the 14th Amendment] contemplates two sources of citizenship, and two sources only: birth and naturalization. The persons declared to be citizens are “all persons born or naturalized in the United States, and subject to the jurisdiction thereof.”
When the 14th Amendment says “All persons...” that includes Presidents and Vice Presidents.