I once decided to do an exercise from a game design textbook. The exercise was to design a simple game around a territory capturing mechanic. Instead of just completing the exercise, I decided to make it possible for people to make and share games that used the same type of board/moves. Finally, the resulting game editor/player is ready to share! I think this could maybe be a good tool for people to experiment with game design.
I would really love it if you would try this out and make some games. I would love it even more if you would share those games with me!