Yes, but from an American perspective (see what I did there?) not to mention many other linguistic perspectives, there is only one thing we call ourselves: Americans. And even if there is a broader usage of that word (there is) the primary usage means someone from the US. Francis was the first Argentinian and South American (more broadly), but also the first pope from the Americas. No one is disputing that. But by saying that the new guy is the first American pope, we are using the generally accepted primary usage of that term. There should be no dispute.
A couple screenshots from Wiktionary (which is very balanced and has lots of languages represented):
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