"is yet, in the words of Lord Coke in Calvin’s Case, 7 Coke, 6a, ’strong enough to make a natural subject, for, if he hath issue here, that issue is a natural-born subject’; and his child, as said by Mr. Binney in his essay before quoted, ‘If born in the country, is as much a citizen as the natural-born child of a citizen, and by operation of the same principle.’"
The text you quote is simply the court quoting other documents in support of the idea that, in English common law, being a natural born subject is based on the facts of one's birth, based on either the place of birth, or based on the parentage. That is absolutely the correct understanding of the legal meaning of "natural born subject" in English common law. That point is not in dispute.
Note that the 14th Amendment, unlike English common law as clearly expressed in the quotes, does not require or establish citizenship based on parentage (although it does not prohibit it, either.) Nor did the court rule that parentage establishes citizenship—which clearly shows that the quoted text was not a legal ruling, but was merely "dicta" in support of the ruling the court actually did make.
So that proves that the US court decision you're quoting is using those quotes it makes from other documents solely to elucidate its reasons and justifications for interpreting the 14th Amendment as meaning that being born in the US, regardless of parentage, makes one a citizen. It was not attempting to define, or make any ruling on, whether or not being born of US-citizen parents makes one a US citizen. More importantly, it was not attempting to define, or make any ruling on, the meaning of "natural born citizen," nor did it use that phrase.
Neither the question of whether being born to US-citizen parents makes one a citizen, nor the definition of "natural born citizen" was at issue in the case. Courts do not rule on matters not at issue in the cases before them, and whatever they happen to say on such matters is dicta, is said only to justify the legally-binding (and perhaps precedent-setting) decisions they are making, and sets no precedents.
The sole issue before court was whether nor not Mr. Wong was a US citizen because he had been born on US soil, in spite of the fact that his parents were not US citizens, and in spite of the fact that the US Code (statutes passed by Congress) explicitly forbade the acquisition of US citizenship to persons born in the US to parents both of whom were Chinese nationals. Since that was the sole issue before the court, that was the sole issue the ruling legally could have decided, and the sole decision the court could make in the case that would establish any legal precedent.