Well technically it also says that in Japan they only display "Sea of Japan" in the local language (Japanese), so displaying just "Gulf of America" in the local language follows. This blog never expected that the USA would be involved in this kind of dispute.
No because americans actually commonly call it the Gulf of Mexico (despite US government fiat dictating it should be called the Super Intelligent Gulf and anyone against that being double plus ungood), Japanese people don't commonly call it the East Sea. That's the difference.
Google Maps shows Gulf of Mexico (Gulf of America) to Canadians - it does properly label Lake Ontario, though. The idiocy isn't limited just to the US.
I'm located south of the equator.