I modded a game (tho not hl) for many years, I come here to opposite this.
I think since the kid is interested in building a game that they designed themselves, it's better to handover a (simple) game engine to him. A game engine enables way more possibilities than modding. You can add multiplayer over websocket/webrtc, you can write your own shader, you can write your game logic however you want etc. All of that without the overhead/limitation of a modding environment.
Also, out in the wild the job opportunity for Garry's Mod developers is very scarce, if any. Just something to think about if op wants to do some carrier development for the kid while having fun.
Oh for sure, I would not suggest doing HL2 Engine Modding, I had suggested it because it has the lowest barrier of entry to get started for a someone that young. Basic Wiremod can make some rather complicated contraptions. and once you start going down the Lua route with a custom gamemode you can just about make anything, I've seen mario clones to RTS done with Garrysmod gamemodes
I see your point actually, I had a lot's of fun in Garry's Mod too playing people's creation.
My previous comment was more like a personal regret on my self that I failed to convert my modding experience into actual skill in game design/programming. I started it too late for me to relearn all the math and etc. I imagine my career will be a lot different if I started with the intention of designing an actual game.
I think since the kid is interested in building a game that they designed themselves, it's better to handover a (simple) game engine to him. A game engine enables way more possibilities than modding. You can add multiplayer over websocket/webrtc, you can write your own shader, you can write your game logic however you want etc. All of that without the overhead/limitation of a modding environment.
Also, out in the wild the job opportunity for Garry's Mod developers is very scarce, if any. Just something to think about if op wants to do some carrier development for the kid while having fun.