You obviously could design the game first and the box afterwards but you may have been given a BRIEF to ask you to design a game around a given sized box.  Assuming the game has to be designed around this box we can make it either by conventional means or by using a CNC milling / routing machine.  These sketches were done on Pro-DeskTop software with the orthographic drawings being done as an option in that software.  It is however a good idea that you know how to do drawings like this without the computer doing it all for you.

Box end - 120 mm x 50 mm x 12 mm

One side panel of the box - 120 mm x 50 mm x 12 mm

You will need two of the part marked B - these are the sides.  You will need one of each of the parts marked A and C ( since one end of the box has to be lower than the other to allow the lid to slide into place.  Then of course you will need a lid and a base.   Check the diagram on the first page
( or below )  if you need help in visualising how it all goes together.

There should be no need for screws or nails - PVA glue will provide a perfect bond and the parts can be held in place whilst the glue dries by using a vice or a sash-cramp.  Make sure glue doesn't get into places it isn't needed.  Apply it using a small piece of wood rather than upending the
container !