It also really bothers me that they get to coin the whole American term when it's a terrible representation of America as a continent, the USA doesn't really even have a proper name, it's a description, kinda like calling a dog Dog. Mexico's full name is actually Mexican United States of America.
I personally call them united-statesian when the word gringo doesn't fit the context, which is the translation of estadounidense from Spanish. But it's so stupid because whatever you call them applies to so many more people than just them because they don't have a name! And their states are not really that united.