A useful distinction
A click, tap and key press are different physical interactions. A control that works conveniently with one may be awkward with another. Designing around the game action first helps identify how each input method should express it.
Put it into practice
List actions such as select, move, pause and restart. Map each to supported inputs and test the actual device context. Do not claim support from the presence of an icon alone; confirm that the action can be performed and its result understood using that method.