Although I don't personally believe that it's true, let's suppose for the sake of argument that internet addiction could be considered legitimate. Although it has become increasingly rare in this ever-more litigious society, it is possible to be fired for an addiction, especially when it impinges on your ability to do your job. Alcoholics and drug addicts (legal and not) are often fired once their addiction is discovered, and it's usually discovered simply because it prevents them from performing sufficiently well at their place of employment. The reason they can be fired is because (hypothetically) they could choose to go into rehab of some kind, and their choice not to do so is relevant. So, if you couldn't control your internet addiction and it kept you from being able to do your job, you could potentially be fired. That makes sense to me.
However, if you count internet addiction as a disability, suddenly workplaces will be required to keep you on even if they find out about it. You can't fire someone for being restricted to a wheelchair, or having OCD, or being HIV-positive. Granted, your employer may, for instance, find a position for someone in an office instead of, say, manual labour, but your boss would have serious legal problems if they fired you for having a disability. So if internet addiction were recognized as a disability, nobody could fire you for it. The problem is, in this day and age, most businesses are highly computerized, so finding a position for someone that doesn't use a computer at all would be remarkably difficult.
So I say it may be an addiction, but for God's sake don't call it a disability, especially a legally-recognized disability. Stupid things happen in upper-management heads when something is called a disability. For example, at a friend's place of work, he had to actively argue against an employee being transferred to reception. The upper-level management couldn't understand why you wouldn't want someone with Tourette's syndrome being the first point of contact for your customers.
Having a disability does not mean that you are inferior, but it does mean that there are some things you simply can't do. However, when something is legally recognized as a disability, in an effort towards equality, too many people try to fit a square peg into a round hole. If someone did not have Tourette's, but had a potty-mouth, would you put them in a receptionist's role? If someone was not in a wheelchair, but was not strong enough to lift heavy boxes, would you hire them as a mover?