PLA is fine for this. 3 Perimeters, 15% Infill… (nothing special)
The X and O-Pieces can be printed in two colors if you want. Just ad a color change at the right layer.

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The holes for the magnets have a diameter of ⌀6,10mm so they should just press in. It can be that yours need to be glued in (or they are to tight).
To store the game you just put the remaining game piece in the middle position (on top of another piece) and then put the Lid on to secure all the game pieces.
The author marked this model as their own original creation.