I'm not the kind of person who thinks nature stuff is inherently superior to electronic stuff. I love trees and hikes, but I can't play Monster Hunter: Generations on a goddamn pine cone. Sadly, as much as I appreciate your child's attempt to catch 'em all or beat up Bowser, anything that beep-boops is better left at home and nowhere near the cabin that they're going to share with 11 other kids. You know what's not the best way to make a first impression on 11 other kids? Being told that you'll probably be allowed to keep your electronic device, and then having it ripped away from you by your parents in front of all of your potential friends.
Forcing a kid to argue with you in public is the worst socializing technique since the invention of the missed high five. There's a time and a place for everything, and Surrounded By A Bunch Of Children Who Will See A Boy Throwing A Tantrum And Stay The Hell Away From Him is not the best place for "Give me that game right ... NOW." Also, on a more practical note, they're staying in cabins and tents -- two places that aren't known for their generous supply of wall sockets. As soon as the battery runs out, that game system becomes an expensive brick that they're trying to save from getting broken.
"You and I are destined to do this forever." -- Nature