Not a parent either, but constraints such as "you can only play videogames that you code yourself" could be an entertaining way to teach: they might want the reward, teach them to enjoy the path as well.

I am not saying they should learn computer science, but it's one of the best ways to use computers, and having some basic skills with it is incredibly useful still.

You can't really do that today. In 1980 Frogger was the state of the art of video games, a kid could code a clone of it over a few weekends so the hurdle was reasonable. However modern games takes years to clone even for professionals, even the indie ones, so you banning them from games they haven't made themselves today essentially means you banned them from ever playing games.

The main problem is that basically everything a kid would want to do with computers is already done in neatly packaged binaries, so the reward for exploring is just the exploration itself. And preventing your kids from using those binaries wont make your kid excited to recreate programs from the 80's, it will make your kid resent you as a conservative parent who wants his kid to relive his own childhood.

Well, there are plenty of game engines out there that empower the user a whole lot. And I bet any kid who codes a simple snake today would still play the hell out of it, and have plenty of ideas on how to improve the game even further.

You are right, however, that some parts are simply impossible to replicate: narratives, for instance, have to be experienced. Gameplay however, is where the fun is when it comes to games and game programming (this might be subjective), and is usually quite simple to replicate.