The only explanation is that the Translator(s) that SNK hired for the game's English release apparently totally forgot that the AOF storyline was set to happen years before the FF storyline did.
That's exactly the case. Mai is not mentioned in Eiji's ending in the Japanese version of the game.
From what some have said, it was an intentional decision not to take the translation seriously at all.
You are also assuming, wrongly, that SNK characters go through stages of life like we do. If that were the case, Athena Asamiya would have passed jailbait status at the time Nests Cartel was still looking for a building permit. And Bao, whoo, do not get me started...
Sorry, but the Comic Book Time typical of The King of Fighters series doesn't apply to the Art of Fighting and Fatal Fury series. Characters in those series did age as their bio sheets showed each subsequent installment. Not to mention that Jeff Bogard was alive during the events of AOF 2; Terry and Andy (and therefore, Mai) couldn't be anything but kids by then (it's even shown in the Wild Ambiton intro that they were indeed very young).
Bio sheets? Wild Ambition?? Seriously? What we have here is numerous parties at various stages of two fighting game evolutions trying out lots of different ideas, most of which would be scrapped, forgotten, or outright retconned. Let's remember that SNK has had an extraordinarily turbulent history. It's perfectly reasonable that later programmers would look at older works, say "the heck with this", and quietly do away with it. (A lot of it is being able to reuse sprites. King of Fighters, anyone?)
Again, that's in KOF continuity only. Compare Geese's appearance in the 2nd AOF to that in FF 1.
I notice everyone seems to say that Takuma's alter ego's name of "Mr Karate" started out as a Fan Nickname sorts. But I'm pretty sure the announcer calls him Mr Karate rather clearly in the very first game when you choose him in Versus mode (Although his name tag shows only "???") What's the full story, anyway?
In the first game, you're not supposed to know who he is, so he goes by the moniker "Mr. Karate" (or, more informally, "The Karate Master"). Less dumb than "Question Mark Guy". In Sv C Chaos, it's morphed into something of an alter ego, which he uses whenever he gets tired of the grind and just wants to go out and kick butt. Yeah. That's about it.