Which engine would be good for a 10 year's old (smart one)? Assuming he would use it for the next 5 or so years (so age 10-16 I guess). For 2D games only (boardgame like).

I would prefer something that forces to learn programming (so not just some boxes you move around and connect) but not something as extreme as C++.

Why only 2d if I may ask?
Also, I'm assuming you would want him fully competent as a game dev at the end of it, with something like Java or C#, so would a game engine with a language like Python be something you'd even want to look at?
 

Also, what is your end goal in all this?

Just an engine for a kid to make some simple gemes in it, like Basic in the times when I was young Something to learn programming.

Because he wants to make a 2D board game Besided, I'm against teaching kids 3D, it turns quickly into heavy "build a team of artists to make the assets" and "focus on renderer" which leads to looong projects that never get finished and masks the real problem "only if I got the assets/people". When you have all the assets made yourself in paint, well, you can't blame anyone else than you for not finishing it Anyway, 2D would suffice.

Wholeheartedly agree with the 3d thing Just wondered how much you want him involved as a programmer when he does get older.
I have a younger brother that's interested in learning code, but mostly he's just fooling around with batch files at this point.
I'd have 2 suggestions for you. Unity or Javascript... C# is probably a little heavy, but I'm personally a believer in letting it sink in over time, and with Unity you would have tons of videos and tutorials that you could sit him down with that would actually let him ease himself into it more slowly.... I'm also a huge believer in establishing a foundation first, so C# would have a way to hard learning curve for that...
JavaScript and webapp games would probably be perfect? Javascript is decently light, and all you'd need is a browser... It would lend itself very well to 2d HTML is a piece of cake even for a 10 yo I would think. I think that's you're best bet. Nothing fancy needed, and Javascript also has tons of learning material online. I've personally never checked out the game dev side of Javascript now, but I know for a fact is very much alive and growing.

Just my 2 cents... I probably have half the experience you do

Some options are scratch, lego mindstorm, python, perhaps things like rpgmaker, but don't know anything about those.

Recently there was an article about making games without heavy programming, it's proably findable in the resources of beginners. Maybe that has a few good ideas.

I was going to stay out of this, but I have to second the suggestion for html/javascript based. <I know, shiver a little> But take the compiler and heavy apis out of it. The creations will be share-able to more friends and family without target prerequisites. Never mind all the horse power if no one (of importance) will see it. I don't think javascript is damaging at all, maybe just a slower(?) start. 

When I was a kid in the 80's I found declaring variables of different types wasn't difficult to understand as necessary but I had a hard time understanding how memory was relevant. It might've taken a little awhile to understand objects and their properties but if all I had to do to get an image to the screen was write one line to load the image and another to blt it to an x,y location on the screen, I would've been in heaven.

So, I think, if you have a language where you don't have to worry about memory management, it's easy to setup a basic loop of some kind, and you don't push the kid (yet) to follow best programming practices, it will probably serve you quite well. C# seems to be a reasonable candidate to me.

Other than that, the only engine I'm at all familiar with would be Game Maker. I tried it out for a bit with the GUI programing interface and it reminded me of a C64 program Arcade Game Creation Kit. I already knew how to program but it was an introduction to things like tilemaps, sprites, and collision events and putting these various elements together to make a game.

I was thinking about (in that order):

Godot

Love

Game Maker

I have never used any myself

I'm a little confused at what your looking at... Godot is fine, I've fooled around with it a bit, but I wouldn't recommend it to a beginner for the reason of how would they learn it?

If they've worked with engines before then fine, but Godot doesn't have even close to the learning resources of lets say Unity or Unreal. Unless you want the kid pouring over docs right off the bat.
I've never used either of the other ones either, but I have found that nothing dries up energy and ambition like running straight into a wall and not knowing how to code you're way out of it. Yes you'll probably be helping him, but I think you're giving him a lot more of those instances then you would with a popular Game engine that one google search later will have him on his feet again potentially. All that really matters is that he's coding, even if he is copying a lot. I think he'll be coding a lot more with a popular game engine like Game Maker since that's on you're list.
Then again, all this is just how I've found my own game dev, so you may think differently
God bless and good luck with your decision... It's like choosing what language to use! ?