The answer to that question is literally what the article is about. Essentially, the Solicitor General argued that the word "domicile" is implied in "reside in". If you're saying that's bogus because that word isn't in the 14th Amendment, than that isn't good for Trump.
Anyone can "reside" here in a "domicile." The definition of "reside" is to dwell someplace permanently in a particular place. It says nothing about legally residing in a particular place permanently. The definition of "domicile" is the country that a person treats as their permanent home, or lives in and has a substantial connection with. Again, the words legally treats or legally lives in isn't mentioned.
Illegals came to this country willingly, and many have been here 20+ years, residing permanently in a particular place, despite having broken the law to come here. That means the children they brought here, or had here, have resided here permanently with their parents in a particular place...just not legally.
At the time, because slavery was legal in this country, slaves, despite having been kidnapped from their homeland, by law, were here legally. Slaves were brought to this country against their will, taken away from their homeland and forced to permanently reside in a particular place, and it was all legal based on law. In many cases, babies born of those slaves were children of slave owners, or other white men who permanently resided in a particular place.
I have no good feelings over this argument, and no hope that the Supreme Court will rule properly on this issue.