People need to learn that gaming itself isn't unhealthy, nor is living mostly or entirely indoors, nor is being sedentary.
The health problems associated with these things, including mental health problems, arise from incompatible combinations of lifestyle, diet, genetics and attitude--never one trait individually.
A pale person is fine with little sunlight. That's why they're capable of being pale in the first place: to create more vitamin D from less sunlight. If pale enough, one can receive as much vitamin D from ten minutes of indirect sunlight as necessary every 24 hours, more than the average well-browned beachgoer does in twenty minutes of direct sunlight or the average Sudanese does in three hours of direct sunlight.
A sedentary person is fine with a low-calorie, high-nutrient diet. It's when they eat like an athlete or worse that it's a problem. It's when you intake more energy than you expend that you build fat. The remaining common problems at this point are avoided with good posture.
The stereotypes of health, hygiene and social skills associated with gamers may be because people with problems in these areas are attracted to physically solitary and physically leisurely activities, but it is not because gaming encourages any of this in those who are already healthy and know a thing or two about human biology.
So long as the camp isn't also feeding them Cheetos and cookies, so to speak, I can't imagine what the hell the problem is with it centering around the high-tech activities we're going to have to cope with sooner rather than later.