Translation:Is American a language?
I'd interpret it as just "American", since American English would be 미국 영어. That's what the sentence is implying.
To form the name of a language, you usually (but not always) add the suffix 어, which comes from the Chinese 語, meaning language, to the end of a country's name. Like so:
프랑스 (France) > 프랑수어 (French)
일본 (Japan) > 일본어 (Japanese)
한국 (Korea) > 한국어 (Korean)
미국 (America) > 미국어 (American)
Of course, there's no language called American (despite what some Americans might claim), but that's the point of the example.
I expected 불어, but I didn't know about 일어 and I'm not the only one over here though it does get shortened even to just 일 in context. 일어 sure does get a lot of hits though. I've never been fond of saying just English and such being vague terms, preferring the English language. So I'm reading this, "Is American language a language?" A completely different interpretation. "Yes, it's a dialect of English." 미국식 영어 is what I'm getting though nowadays maybe the 식 would be dropped. In Japanese that's often shortened, along the lines of 미어 or even just 미. British and American English together would be called 영미 어. Hey, it showed up on Google Translate just now. In Japanese it's even used in names of university departments and whatnot, no mention at all of other countries . . .