It's a great idea of a game combined with educational process, and I must admit it was really interesting!
I saw this idea here in our @HomeEdders community where 
You baby is younger than mine, so you used 2D variant, my boy needed something more complicated so I changed and developed your idea a little;) We added 3D shapes and some more complicated shapes in 2D.
And the idea is perfect because we can change it for different needs and wishes.
So we took sticks and plasticine as well and tried to create shapes written in the paper.
It was geometric shapes.
Then it was letters
ANd finally we had fun creating different rockets and fantastic shapes;)
Now my son knows and understands what the difference between a cube and a square is:) Nothing is better than creating them by your own hands.