The titular question seems like semantics to me. The video game "addicted" men featured clearly had some kind of problem if they all think they would have killed themselves without treatment. Whether or not we call it addiction, the treatment was/is worthwhile, right?
I think the more interesting question is: do we need to regulate video games more? In other words, how big of a negative impact are video games having, utilitarianism-style? It sounds like many South Koreans think the impact is big, big enough to pass a pretty intense regulation (https://en.wikipedia.org/wiki/Shutdown_law). Here's another NYT piece (https://www.nytimes.com/2017/04/01/opinion/sunday/video-games-arent-addictive.html) that argues the other side.
This article also doesn't touch the way video games can use micropayments to farm revenue from hooked players (https://levelskip.com/misc/Skinners-Box-and-Video-Games).