No she didn't.
The question is presented in this case whether, since the adoption of the Fourteenth Amendment, a woman who is a citizen of the United States and of the State of Missouri is a voter in that state notwithstanding the provision of the constitution and laws of the state which confine the right of suffrage to men alone.She argued that as a citizen, the 14th Amendment gave her the right to vote. Big difference.
You need to go back and read the next couple of paragraphs. You missed the basis of HER ARGUMENT:
The argument is that as a woman, born or naturalized in the United States and subject to the jurisdiction thereof, is a citizen of the United States and of the state in which she resides, she has the right of suffrage as one of the privileges and immunities of her citizenship which the state cannot by its laws or constitution abridge.
The part in bold above is the citizen clause of the 14th amendment. If she wasn't making this argument, then you'll need to explain why the Minor court said:
The Fourteenth Amendment did not affect the citizenship of women any more than it did of men. In this particular, therefore, the rights of Mrs. Minor do not depend upon the amendment. She has always been a citizen from her birth and entitled to all the privileges and immunities of citizenship. The amendment prohibited the state, of which she is a citizen, from abridging any of her privileges and immunities as a citizen of the United States, but it did not confer citizenship on her.