Actually, anime is a real style, believe it or not. If you got oh say, a Mickey Mouse translation from Japan, that would not be an anime. There is a difference between cartooning and anime.
I don't consider Pokemon an anime because it is over-franchised and while it may have a midway style between cartooning and anime, I have never considered it an anime and never will.
And some anime styles don't actually have big eyes. Those would be the complicated ones.
But as for the serious plot, would you call Pokemon serious? I mean, really. xD