As a few people have already stated, games may not necessarily be addictive in and of themselves (in the way that drugs are chemically addictive), but they are designed in such a way that people with addictive personalities. Addicts are attracted to things that instantly stimulate the reward/pleasure centers of the brain, and things like drugs, gambling, sex, gaming, and even shopping can all set off those centers.
For the most part, the dividing line between "hobby" and "addiction" lies in whether or not your gaming, drinking, gambling, etc. become detrimental to the rest of your life. If you miss work or school because of gaming, you may be an addict; if you lose touch with friends and family because of gaming, you may be an addict; if you're often broke due to the amount of money you spend on gaming, you may be an addict. From the sound of it, you're not an addict. Next time anyone tries to corner you and call you an addict, compare your gaming to having a drink or two at a party or to unwind after a long day, or something similar. I'm sure that other people in your family have hobbies that they engage in, but not to excess; provide them with an example from their own lives to try and give them a bit more perspective.
Oh, and simply saying "I'm not and addict" with little or no supporting argument never works. If this is what you have to deal with, then you need to spend some time thinking up clear, logical defenses and concentrate on not getting aggressive when your family confronts you.