The initial personal attack aside, it is simply fallible to say that there is no mental aspect to addiction. Hell, if there weren't a mental component, articles like the one posted would never, ever happen. Addiction of MMORPGs, or the internet, is almost completely mental.
One of the major things they teach you when you're dealing with alcohol addiction, be it with the twelve-step program or general rehab or individual therapy, is that it IS an illness. Not just a physical illness, but a mental one as well. If it was simply physical, one you quit it'd be easy to stay off it... but it's not, because it's in your head too. Nor would there be a significant component to psychotherapy devoted to the treatment of addiction.
Now, I think there are two problems here.
The first is the connotation of the term "mentally ill." While the term traditionally applies to people who have severe mental illness, such as schizophrenia, by no means are those the only mental illnesses. That is like saying someone with a cold isn't sick, because they don't have cystic fibrosis. Like physical illness, mental illness spans a range of degrees, from very minor to extremely severe. Addiction can fall anywhere on that spectrum, since the severity of the disease is highly dependant on what it is you are addicted to.
Second is that there is a significant social stigma when dealing with mental illness. How many times have you heard someone make a joke about Prozac (or another anti-depressant) in the last week? Mental illness, of any degree, is highly derided. Going to see a therapist is something that people just don't talk about, yet seeing a doctor might be mentioned out of hand with no regards for something thinking poorly of you. Perhaps the only real acceptance of it is marriage counseling, which I attribute more to the influence of Christianity on society than anything to do with psychotherapy.