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."