Totally Immature, Childish GM's. Literally.

I have done my job well. I have two sons, both of whom navigate the seas of geekery with expertise and cool aplomb, and neither of them are burdened with the lingering self-conscious nerd-shame my generation was cursed with. I could end up living in a six-by-six cell under Guantanamo, and still consider myself a successful father for that alone. They like what they like, and be damned the nay-sayers.
My firstest-bornedest is sixteen, and, while not a role player, takes all of ten minutes to quit bitching about "having to play another one of Dad's stupid playtests" and totally gets into the game. He's the one that wants to keep going after four hours, and he's the one that will drive a totally dice-less session of Savage Worlds. My secondest is eleven, and he's my gamer. He plays in anything I make, along with a weekly group at his school. He paints minis and knows what a bec de corbin looks like. And he's wanted to GM since he was six.

These Nerds are tasty. Almost as tasty as
your character's slow and painful death.

THE EVOLUTION OF A GAME-MASTER
Of course, he started with wanting to push minis around on a dry-erase game mat. What the hell, he was six, right? We'd lay out a handful of the old plastic D&D minis and break out the markers and go to town. When a particular mini didn't fit the bill, out came the Lego dudes. That's Stage One: chaos on a table-top.

 "You kick open the door and there are eight Beholders!"
"Eight?"
"Yeah, I saw them in your book and they look cool."
"I run away."
"You can't. Uhh...the door shuts and locks behind you."
"Can I talk to them?"
"No. The first one floats up to you and turns you to stone with his eye attack!" (cackling laughter)

Stage One is rules. His rules. And accessories. What I realized during this phase, was that the kid was story-telling, but he wanted rules to enforce his plot idea. We'd spend hours with him basically telling me what I did and what happened. When anything deviated from what he had in mind, he'd throw monsters at me and fake-roll dice to tell me how everything magically got back on track.

Worship me, children. With dice.

I've played games with adult GM's who still live in Stage One.
Stage Two was "I love X/Y/Z and want to make a game about it". This is where the kid got infatuated with a particular IP, be it Halo or Fire Emblem or Pokemon, and saw a tabletop RPG as a way to get more of whatever it is. Again, lots of arbitrary rules, but not to rail-road his idea of a story; instead, he was actually designing rules, with increasing consistency, all geared toward capturing elements and flavor of his obsession du jour. This stage is all about detail, tons of detail, and the whole point of playing is to recreate the IP.
I've played with adult GM's who do this. Hell, sometimes I do this. Almost every futuristic military campaign I've ever written is an attempt to game-ify James Cameron's Aliens Colonial Marines.

Stage Three arrived this year. That's where it all starts to come together, and Actually Fun to Play becomes a real consideration. He surprised me with a zombie-apocalypse game that grew out of Call of Duty Nazi Zombies, and ended up being a RP-light mostly-board game that was shockingly fun to play.

Disclaimer: don't get me wrong. It's fun playing with your kids. Better than fun. It's part of the tapestry of them growing up that you'll look back on when you are old and crusty and incontinent and it's absolutely frigging priceless. They do silly things, and it's fun to watch their little brains work. But, in the early stages...let's be honest: if it wasn't my kid I was playing with, it would have been excruciating. Which brings me (finally) to my point:
Pretty much every stage in the kid's gaming career is a legitimate way to game. The kid was on track with what a lot of adults pass off as gaming. The big difference between the kid and the adult is two fold: first, fun for players wasn't a concern when he first started. He was having fun, and of course that means it's fun for everybody, right?

Except this guy.
He thought the combat mechanics sucked.

The second thing that made his early games 'immature' was strictly that: he was immature. He lacked experience, and (most especially) the tool-box that a good GM brings to the table. A good GM can rail-road a game just as egregiously as any six year-old, but she has the back-log of plots, stories and situations to camouflage the rail-roading. A good GM can artfully lay out options that really aren't options, and can gently nudge the random actions of players back on story-track.

So I guess my advice to any dual-class parent/gamers out there is to let the little monsters have fun. Let them run amok and run rough-shod over the concepts of rules and balance. Let them trap you in a room with eight Beholders.

Because what I've discovered is that kids don't really need much teaching when it comes to gaming. They already have it figured out. They just need practice, and to build that story-telling tool-box. And the best way to encourage that is to keep having fun.