Translation:He is swimming to the United States.
I'd say that "the US" is probably a more widely used abbreviation than "the USA" in Ireland, and people would only say "the United States of America" if they were trying to be formal - in fact "the States" would probably be more widely used than the full title.
My guess is that very few people in Ireland would even be aware of "the United States of Mexico".
USA is an acronym for the United States of America, which isn't the phrase that was used in this exercise. na Stáit Aontaithe is the United States - i.e. the US, not the USA.
(On a side note, the acronym for The United States of America in Irish is SAM - Stáit Aontaithe Mheiriceá)