Honestly, the reason some people out of work play video games are more likely one of the following:
1. They're fun and they reduce the tedium of everyday life. Others could do the same thing with sports, tabletop games, chess, TV shows and movies, etc. There's no practical difference between an unemployed guy playing video games all day and the same person watching TV all day or playing golf all day. It's merely a way to take your mind off all the boredom while looking for a job.
2. Playing games can in theory be a way out of poverty, at least in today's internet social media driven world. How many of these people have YouTube channels or popular presences online? If you have no other practical options, then trying to make money through video game Let's Plays and YouTube monetisation seems like a decent last resort.
And yes, the job market is broken too. Maybe if companies stopped trying to look only for people with every skill and piece of expertise needed in advance and were willing to train people to do jobs, we might have less people unemployed at the moment. Heck, maybe the New York Times could help here. Stop doing the common media thing of mostly hiring upper class college graduates from privileged families (which seems to be a trend at the moment) and start hiring people who want to work rather than those who whine about how poor people act in internet editorials.