I don't think the article you posted from Townhall is a quality legal argument and it's not even very well written. It would be nice to see a better review of the meaning of "natural born" from someone who knows how to do Supreme Court level legal and historical research.
I'm open to the possibility that Obama is ineligible. But I don't think that your argument or that of the article would be sufficient to prove this in court.
You may have heard that Chester A. Arthur's father was not only born in Ireland, but was not even a citizen when Arthur became president. Maybe Arthur should not have been president, but for some reason questions about this always revolved around his possible birth in Canada rather that his father's citizenship - until this year.
I think it is very clear. Every President was born on this soil. In the beginning, their parents were not. The Founders did not want a President with divided loyalties. They had proved themselves and suffered to form a united nation. Later Presidents wouldn’t have that kind of proof.