To Publius: No, you’ve got the wrong clause. The one discussed, and the one at issue, is found in Art. I, sec. 9, as the author stated.
To Ben: The clause applies to any “(p)erson holding any Office of Profit or Trust under them, ….” To my understanding this clause has always been considered as applicable to the President. As the lengthy opinion in re. Obama’s Peace Prize reflects.
As the article noted, there is no case law to aid in interpretation, and application of this clause. Given Trump’s vast financial holdings (and entanglements?), and his penchant for keeping it all mysterious, this might well change in the near future. It can be argued that the President-elect’s personal finances and interests presents precisely the issues, and the attendant appearance of improprieties, that the clause was intended to address.