Sorry, but that's a pretty terrible definition of mental illness. Mental illness can be any case where your mind has fallen into a pattern of being chronically unhelpful to you; this can mean it doesn't report on reality correctly, or that it sends incorrect (or merely destructive) emotional signals, or whatever else.

That said, this is one of the reasons I like to think of it as "mental health" rather than "mental illness". It's more like weight/nutrition, where a person doesn't simply have a problem or not have a problem; it's a sliding-scale. Everyone's mind benefits from care, the degree of one's challenges just varies based on personal history and genetics.