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Mechanic design means the design of the game mechanics and gameplay. As such every game needs it to, indeed, be a game.
Simply put mechanic design covers the systems and rules the player interacts with. It is an extension of interaction design for games
There are many ways to go about designing mechanics. Just slapping mechanics together haphazardly leads to a loss of focus and coherence. This is why it’s a good idea to have a guideline/rule to drive the design in a chosen direction.
Some of these guidelines are addressed in the supplementary design drives page.