This is the Modern Chess Set, and, as you can see in this illustration, this Chess set is able to fit very compactly in this tiny box.
You will notice the pawns are these little cubes that fit together well. The rooks are a little larger and do the same thing. The bishops and knights have some sort of symmetry, to create a rectangular solid, I like how the king and queen dovetail together, as it is rather poetic, in a Freudian way.
I am assuming that the chess board is not there, but it looks like it would fold up and fit inside this box. In fact, I just checked my Source, and there is no board included. I’m sure you have probably seen this on the photo, but the pieces are made of maple or cherry wood. Remember that white goes first.