[kabar]

Wouldn't this alone make him ineligible to hold the office of the presidency?

No. A U.S. citizen may acquire foreign citizenship by marriage, or a person naturalized as a U.S. citizen may not lose the citizenship of the country of birth. U.S. law does not mention dual nationality or require a person to choose one citizenship or another. Also, a person who is automatically granted another citizenship does not risk losing U.S. citizenship. However, a person who acquires a foreign citizenship by applying for it may lose U.S. citizenship. In order to lose U.S. citizenship, the law requires that the person must apply for the foreign citizenship voluntarily, by free choice, and with the intention to give up U.S. citizenship.

[SERKIT]

Naturalized not the same as natural born.

[Stingray]

A U.S. citizen may acquire foreign citizenship by marriage, or a person naturalized as a U.S. citizen may not lose the citizenship of the country of birth. U.S. law does not mention dual nationality or require a person to choose one citizenship or another.

The information you cited is from a site that deals specifically with international travel, and makes no distinction between a "natural born citizen" and a "naturalized" one. It only talks about citizenship.

Article 2 Section 1, on the other hand, does address the requirements of being eligible for the presidency of this country quite specifically.