One good suggestion is multi-user dungeons (MUD). They are text-based games that are open source (free), developed in multiple languages including C, C++, java, python and more. They are also online multiplayer games that pretty much gave birth to the whole massively multiplayer online games such as Ultima Online, Everquest, Dark Age of Camelot and of course, World of Warcraft.
A MUD (/ˈmʌd/; originally Multi-User Dungeon, with later variants
Multi-User Dimension and Multi-User Domain),1 is a multiplayer
real-time virtual world, usually text-based. MUDs combine elements of
role-playing games, hack and slash, player versus player, interactive
fiction, and online chat. Players can read or view descriptions of
rooms, objects, other players, non-player characters, and actions
performed in the virtual world. Players typically interact with each
other and the world by typing commands that resemble a natural
I've personally used MUD's to learn how to program, game design, manage an online game, manage an online community and test. This allowed me to transition into a video game job, where I worked in the video game industry for 8+ years working on specifically online games.
Although I ended up more on the marketing/publishing side of the industry, MUD's prepared me enough to both understand the core fundamentals behind a game, as well other aspects of that allowed me to hit the ground running and opened up a lot of doorways to other game engines at a very young age (15 to be exact).
You can install MUD's on pretty much any operating system these days, but it's recommended for Linux/Unix based stacks. You can download a free source of any type of MUD engine from the MUDBytes website. I highly recommend a Diku/ROM based MUD to start with that is programmed in C.
Remember, MUD's can be just as complex and robust as any high-quality AAA MMORPG in terms of game design. They just lack high-end graphics and sound. So, you can split your kids up into separate teams to represent separate departments on a game including game design, system design, QA and then start working on a game they can grow and play.