Not really. It was not about Natural Born Citizenship. Only citizenship.
From the majority opinion of Justice Grey, the question to be resolved:
It is conceded that, if he is a citizen of the United States, the acts of Congress, known as the Chinese Exclusion Acts, prohibiting persons of the Chinese race, and especially Chinese laborers, from coming into the United States, do not and cannot apply to him. The question presented by the record is whether a child born in the United States, of parents 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 by virtue of the first clause of the Fourteenth Amendment of the Constitution,
Nothing there about "natural born citizen".
Then the conclusion:
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.
Nothing there about "natural born citizen" either.
And in fact in the quote from Binny a distiction between a child of an alien born in the country and the natural born child of a citizen is made. Plus, and I just noticed this, so thank you for pointing me at "WKA" again.
During the debates in the Senate in January and February, 1866, upon the Civil Rights Bill, Mr. Trumbull, the chairman of the committee which reported the bill, moved to amend the first sentence thereof so as to read,
All persons born in the United States, and not subject to any foreign power, are hereby declared to be citizens of the United States, without distinction of color.
Mr. Cowan, of Pennsylvania, asked, "Whether it will not have the effect of naturalizing the children of Chinese and Gypsies born in this country?" Mr. Trumbull answered, "Undoubtedly," and asked, "is not the child born in this country of German parents a citizen?" Mr. Cowan replied, "The children of German parents are citizens; but Germans are not Chinese." Mr. Trumbull rejoined: "The law makes no such distinction, and the child of an Asiatic is just as much a citizen as the child of a European." Mr. Reverdy Johnson suggested that the words, "without distinction of color," should be omitted as unnecessary, ...
Thus persons born of alien parents were spoken of as being "naturalized" by birth in the US, not being "natural born" by virtue of such birth. At least in 1866.
The important point, besides the history and record of the court, is that there has never been another interpretation of natural born citizen in Supreme Court proceedings. There have been some idiotic circuit court decisions, but they demonstrate that this is about power politics - “the persuasion of power” described by Andy Stern - rather than legal reasoning.
Since you portray yourself to be so smart on the subject, why do you not tell us what Wong Kim Ark has to say about what a “natural born Citizen” is rather than just citing it.