I don't know why you quote this. It seems to contradict itself. The term is convenient for people, plus SNK themselves have used it.
I don't know why you keep saying it's an American thing.
It's because the "Entertainment System" or "Video Computer System" monikers and the corresponding three-letter abbreviations were mainly American inventions in the late 70s and early 80s (Atari - VCS (later on renamed to 2600 when the 5200 came out), Nintendo of America - NES) and SNK copied it for their homecart systems to cover that but originally never used "AES" for systems or games, it was either MVS or NGH or Neo-0 or Neo ROM, etc.
When I say SNK, I'm referring to the real SNK, 1978 - 2001. I don't give a flying fart on what the current lads and lasses call it.
No, it doesn't matter one bit in the grand scheme of things, I'm just kinda sorta anal about it for no other reason than being old and silly I guess.