You can think of addiction as an intense devotion. Devotion is defined as great interest in a particular thing to which a lot of time is devoted. Gaming could be one of these 'things'. Now if one is able to stop playing games long enough to do these that are more seemingly important than the individual is not addicted. However if this subject tries to avoid having to stop engaging in game-play or tries to solve problems in a rudimentary way to decrease the amount of time wasted when he could be playing the games then he is addicted. Excellent question.
Due to the fact that so many teenagers and young adults are obsessed with video games, you can obviously see that it is an addiction. Remember when GTA 5 came out? All the memes and countdown days? Yeah you could say that gaming is highly addictive. I mean, why else would people play it? Because they hate it? Yeah, that makes sense.
I notice that if I am gaming, during the periods I'm not gaming I am more aggressive and snappy. However, I think it becomes more of an addiction when you start to choose games over social events, homework, sleep, or your actual career. I find that when I see my friends who weren't able to play games for a solid amount of time, they are kinder and happier. Just my perspective though.
I should first identify what an addiction is before presenting any other evidence. An addiction as defined by Merriam Webster is " a compulsive need for and use of a habit-forming substance characterized by tolerance and by well-defined physiological symptoms upon withdrawal".
This definition leads gaming to be identified as an addiction, but it is not as black and white as the context of this question is putting it in. Gaming itself is not an addiction. A gamer can however, be addicted to gaming.
The essence of it comes from how the addiction is created and why we keep it. If what keeps a person from quitting smoking is the desire for nicotine, then the addiction is due to a dependence on the substance. If what's stopping a gamer from quitting gaming is solely his desire to continue playing, then the addiction is attributed to a purely psychological dependence. There is of course a lot of grey area, but it is better to cover it in a much larger post.
Gaming by itself (like gambling) is not an addiction, but you can become physiologically dependent on the stimuli from gaming (like gambling), therefore while gaming in it of itself is not an addiction, if someone were to somehow become physiologically dependent on the stimuli, than gaming would be an addiction.
Or movies? Or music? Or porn? Or gambling? No, they aren't. None of these things can are an addiction, but they can be addicted to. Games are the same way. I remember once hearing the quote that more people die from water intoxication to video games. So, if I wanted to I could probably argue that even water is a more harmful 'addiction' over video games. Honestly, it seems to be that basically anything can be abused these days.