Genetics contributes a predisposition, but something else is needed.
Boredom can be part of that "something else," but without a genetic predisposition you get transient recreational use. It's a habit, perhaps, but not an addiction in the physiological sense.
Another pointed out PTSD. So not just boredom, but stress. (Lump them into "unhappy," if you want; while that may turn out to be the right category, it's probably best to break unhappy into a lot of discrete subcategories for the actual analysis. Otherwise a lot of important details might be glossed over.)
This assumes this study was replicated properly and conducted appropriately. Too many psych studies only report positive reports, engage in data dredging and selective post-hoc analysis. Too many fail the replication test--and when they fail the test, the results of the failure typically aren't reported. So some lab group somewhere knows to ignore the study, but shares this, at best, informally, so the study isn't ignored.
The cynical, ill-will side of me wants to say that this study is pointed out now just because it's a way of saying, "Hey, don't blame me--blame somebody else." I know a lot of kids who use drugs. Fine, they use drugs because they're bored. Not clear what to make of that bit of information. Some are fairly wealthy, but that's probably not the group being defended even though the same defense works for the well-off as for the indigent. Even the fairly poor bored have few excuses. There are a lot of things to occupy one's time.
During the summer my family and I have few resources for things like trips, movies, etc.; the families across the street are the same. Yet we avoid boredom fairly easily. I read, surf, find a lot of things that work for me. Same for my wife and kid. The kid will be learning more viola (since I'll be brushing up on my violin skills and can teach him a thing or two.) Many of the neighborhood kids play video games or play sports in the street. Some have music they make instead of just passively experience. Any average kid who is bored is bored for family or cultural reasons: curiosity's been squashed out of them or is considered inappropriate and stigmatized or they're otherwise prevented from doing things that they find interesting. There are free activities sponsored by local community groups; parks; botanical gardens; libraries. All within 10 minutes' drive, and since this is the 'burbs, everybody has at least one working vehicle. (But many parents refuse to take or make the time, even on days off.) When I was a kid I saw a lot of this. "Let's __________" was greeted with, "That's lame" or something else dismissive. It wasn't cool. My friend and I would swim, bike-ride, play board games, produce the chemicals for small explosive devices.... Our mutual friends thought all of those things boring. No bragging rights there. My friend in his junior year in high school helped build a radio station; our mutual friend became a drug addict because, well, electronics was lame. The electronics guy has a prosperous consulting company, as his hobby became his major became his career; the drug addict had 4 kids by 3 women in two marriages and a spate of failed (then one successful) suicide attempts. The drug-addict-to-be had the wealthier family.
Boredom is like stress. We like to think that kids in poor families have greater levels of stress. We look at income as a proxy for stress. But stress is physiological, the way the studies linking educational achievement or cognitive load and stress define it. The few studies that look at actual stress-hormone levels find that they're remarkably consistent across income levels. The kids of rich parents feel as much physiological stress as the kids of working class families. (Things are different with the truly indigent, those who aren't "food insecure" but "hungry", those in the bottom 5% or so.) Kids make their own stress; kids make their own boredom.
Odds are that another important variable will come to light: Sensation seeking. I don't seek thrills. If I did, my summers would be excruciatingly boring. Not because of anything but thrill-seeking. Not all kids are "normal." Some are at the high end of the thrill-seeking scale.
And since we've already decided to expand it from "bored" to "unhappy," the same is true for happiness. The poor are about as happy as the rich--with the caveat that it's really hard to pin down a good definition of "happy" and get people in surveys to apply it. Happiness seems to be mostly unrelated to income and possessions. My mother was intensely unhappy as a homeless single mother; when she had a paid-for 2000 sq ft house in a nice area, pool in the backyard, gold-plated chandelier and she and her husband had interest from $800k in savings to supplement their $50k/year retirement income she was no less intensely unhappy. (She also had no addictions. When cigarettes hit the price point she'd decided was the most she'd pay, she quit cold turkey when her supply ran out. That was in the 1980s. She's still alive.)
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