Well, if you hit a point where it's interfering with living a healthy and constructive life, then yeah, I can kinda see how it can be labeled as a mental illness. It's illness doesn't have to mean you have a disease, it can simply mean that you are not well, and in the case of internet overuse, there aren't any drugs involved, so it's basically your state of mind that is causing the illness.
the only problem I have is that it no one knows where to draw the line, not even the psychologists, so even if your net usage just happens to be above average, people will start pointing to it as some proof of a mental illness.