This is why amateurs shouldn't cite case law, they invariably get it wrong.
You clipped but a sentence from Ark that is taken from a citation of Minor v. Happersett used by the opinion's author to address an earlier opinion by Justice Miller surrounding the Slautherhouse cases as they relate to the 14th, and is not part of the legal holding. Moreover, earlier in that same majority opinion, the author writes this when tackling the origin of the definition of "natural-born"...
"It thus clearly appears that, by the law of England for the last three centuries, beginning before the settlement of this country and continuing to the present day, aliens, while residing in the dominions possessed by the Crown of England, were within the allegiance, the obedience, the faith or loyalty, the protection, the power, the jurisdiction of the English Sovereign, and therefore every child born in England of alien parents was a natural-born subject unless the child of an ambassador or other diplomatic agent of a foreign State or of an alien enemy in hostile occupation of the place where the child was born."
and more later in the opinion...
"The later modifications of the rule in Europe rest upon the constitutions, laws or ordinances of the various countries, and have no important bearing upon the interpretation and effect o the Constitution of the United States. The English Naturalization Act of 33 Vict. (1870) c. 14, and the Commissioners' Report of 1869, out of which it grew, both bear date since the adoption of the Fourteenth Amendment of the Constitution; and, as observed by Mr. Dicey, that act has not affected the principle by which any person who, whatever the nationality of his parents, is born within the British dominions, acquires British nationality at birth and is a natural-born British subject"
and finally, the holding found in the last paragraph...
"The evident intention, and the necessary effect, of the submission of this case to the decision of the court upon the facts agreed by the parties were to present for determination the single question stated at the beginning of this opinion, namely, whether a child born in the United States, of parent of Chinese descent, who, at the time of his birth, are subjects of the Emperor of China, but have a permanent domicil and residence in the United States, and are there carrying on business, and are not employed in any diplomatic or official capacity under the Emperor of China, becomes at the time of his birth a citizen of the United States. For the reasons above stated, this court is of opinion that the question must be answered in the affirmative."
Now, what does that all mean with respect to young Mr. Ark's ability to become the President of the United States. Well, if you want to know what the dissenters believed to be the practical consequence of the majority's opinion with respect to Presidential eligibility, one only needs to read this paragraph from Justice Fuller lamenting the very reality created by the majority's opinion...
"Considering the circumstances surrounding the framing of the Constitution, I submit that it is unreasonable to conclude that "natural-born citizen" applied to everybody born within the geographical tract known as the United States, irrespective of circumstances, and that the children of foreigners, happening to be born to them while passing through the country, whether of royal parentage or not, or whether of the Mongolian, Malay or other race, were eligible to the Presidency, while children of our citizens, born abroad, were not."
Fuller hates it and thinks its unreasonable to conclude as such, but he recognizes this is the conclusion of and the resulting legal reality created by, the majority opinion in Ark.