I've seen it occasionally used to refer to Americans, because technically speaking, any citizen of any country of North or South America is an "American", and yet citizens of the USA don't recognize this.
To many, the implicit assumption that USA strictly equals America and vice versa is just another artifact of the arrogance built into US culture.
Use of the term "American" to describe US citizens is quite common outside the US.
To me, the idea that this is somehow a manifestation of our cultural arrogance and not just a mundane example of the malleability of human language is just another artifact of how certain people really, really want to find more reasons to hate us.
It's the word or similar to the word for the USA in a few languages, like Esperanto ("Usono": the USA, "Usonano": a USA citizen, "Ameriko" already being used for the continent and "Amerikano" for people from that continent). It was a term introduced in the 1800s without a lot of success, then after its use in Esperanto it was mildly popularised by American architectural legend Frank Lloyd Wright, who embraced the term and described his work as "Usonian architecture" and wrote at length about "Usonian character."
To many, the implicit assumption that USA strictly equals America and vice versa is just another artifact of the arrogance built into US culture.