I'm not buying this one to be entirely honest. Given all the attacks on video games I can understand the desire to point to studies to show positive effects from gaming, as well as negative ones. This study in paticular could be used as a counter point to President Obama's attacks on video games for causing health issues. Lionizing a study like this makes us look just as foolish as people who do the same with studies that we ourselves attack.
Over the years there have been many attempts to brainwash kids into eating/liking fruits and vegetables through the years. This ranges from commercials and "public service annoucements", to bits in cartoon shows (or even cartoon shows with this as a major subject), things in comic books, etc... What's more I'm pretty sure "healthy eating" has been the subject of video gaming software going back as far as the "Apple II".
A big part of the problem with the issue is that people's bodies simply change as they get older. What's more tastes vary. While there are kids out there to whom vegetables might taste good, for most they really do taste pretty bloody awful. Kids don't just decide "OMG, I don't like this because of propaganda" when really you don't see any programming telling kids not to eat vegetables. They wind up not liking it because to them it tastes bad. Understand that kids go through a time period where they will put just about anything into their mouth, and that is going to include vegetables. A lot of vegetables do however suffer a problem due to the simple fact that they reek awfully to kids due to similar issues with their sense of smell. As some studies have shown, one's senses are oftentimes linked, something that lets off a reek can actually influance how other senses interpet it.
One of the contributing factors to things is also the availibility of food. Decades or centuries ago, survival instincts dictated that people (including kids) would eat whatever they needed to in order to survive. With things like meat being expensive and unavailible, fresh vegetables and the like were a stable of the diet. Today that is no longer the case, and even at an early age kids "know" that there are other things availible.
Solving a problem like this isn't a matter of presenting it in an exciting enough context. Just the same as someone who finds math boring isn't suddenly going to enjoy it more if you make a game with spaceships called "Math Blaster" or whatever that still comes down to solving math problems. Kids aren't as stupid as many people things.
Issues like getting kids to eat vegetables come down to issues like parenting and forcing kids to eat things that they don't want. A pain in the arse, and always a hated part of child rearing, but nessiary. It's just like parents taking the time to review video games before letting their kids play them, being a parent is not "easy". What valid problems behind this are generally societal and involve things like how we now require dual-income households and there aren't many parents taking the dedicated role of homemaker/child rearer all that much anymore (and it's a full time job), that's an issue to which there are no easy solutions.
When it comes to things like exercise, that is again a societal problem having to deal with diverse factors like it being impractical for kids to go out to play anymore (due to the danger, or local laws preventing roaming, unsupervised youth without parents around to keep an eye on them). The issue of advanced, first-world nations becoming increasingly sedimentary is also an issue that goes well beyond children all the way up to adults, and again requires addressing big issues of the sorts people want to stay away from.
On the subject of exercise, people also have to seperated intellectual realization from reality. As nice as it is to think about people respecting other people for attempts at self improvement, understand that "fat people trying to work out" is a popular area of physical comedy, and nobody wants to be the but of other people's jokes. Like it or not, most people don't have access to areas where they can work out effectively in solitude.
On top of this, people tend to overlook that coming back from being fat is not an easy thing to do. It's not a matter of someone "not cramming that whole cake into their mouth" or whatever. To work out you've got to do it carrying all that weight until it burns out and it hurts far more than the whole "feel the burn" thing enjoyed by people already in decent shape. What's more, people talking about all those "little lifestyle changes" seem to miss the entire point that people who wind up living sedimentary lifestyles (which is more the cause them over eating) do that because it's how life turned out for them. Finding even 20 minutes a day to work out is NOT going to be an easy thing to do, especially when you consider stress and the toll that the modern work place can have on someone. People happy with their lives (who tend to be in better shape to begin with for a lot of reason) just don't "get" what it is to be stuck in that kind of a rut, sit in a cubicle or stand around all day while being psychologically abused and constantly worried about losing your job, and then stumble home with only a couple of hours to try and rest and recover. If you've got kids in there too, it's no wonder people get physically destroyed.
On the subject of kids, the same basic logic applies, but is worse. The "fatty" can't just go running out to play with the other kids and be welcomed. No, he's going to be mocked, the last one picked (if at all), chased off, and all kinds of other things. As an adult sitting outside of this, it's easy to say what someone else should do, but such people are detached from the reality and wouldn't do it either in the same place.
What is almost lulzworthy is in the places where you have situations where there is an obesity epidemic at a school. In a lot of cases like that it's not due to a lack of focus on nutrition, or bad PE programs, it's simply a matter of the surrounding area and what the kids in that area around the school wind up living like (again coming back to societal issues). Not to mention the whole issue of "keeping the youth occupied" which has come to occupy more of the focus of schools than actual education (another big issue). One of the reasons why education in the US and other countries suffers is because the rate of education doesn't match the rate at which kids learn, and becomes increasingly slower as it's held up to deal with special needs students. What's more repetition in a lot of things exists not just for the learning process, but to keep the kids focused on something. You keep the kids in class for six hours a day, plus sometimes as much as two hours on a bus each way (depending on thing like relative location to the school), then an average of an hour per class worth of homework (if not more, depending on the teachers) you wind up with kids tied up for like 16 hours a day with school, that might not actually be teaching them anything new (which is why a lot probably wind up blowing it off). This is intentional so kids won't go roaming the streets (see "why don't kids go out to play much anymore" another societal issue).
All of this can be argued, and yes I'm making a weighted arguement (pun intended) the point is that no amount of "working out is fun! play sports!" propaganda makes those things viable.