Inside the US, we don't refer to ourselves as "American", we seem to go by whatever the hell our descent was, but outside of the US we refer to ourselves as "American".
Is America the only country that does this?
Also, on another note: To all you who are not native English speakers: When you buy a videogame, do you play it in English or your native language?
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Hmm, it's not quite the same in the UK, generally, at least in England, we'll introduce ourselves as British to people outside of the UK, but if I were to talk to a Scotsman or a Welshman, I'd call myself English. It's all situational.