The ways and rules of play.
If a game is a series of challenges, how much more is it to not put this as your priority in designing it? Let's talk about designing mechanics of games that made up the different challenges. Be it's inspiration based off the visuals, game writings, audio or a scenario, always remember that input is the king of all.
The process of defining a game's core mechanics must be largely based off it's input controls. It is when you start working with the inputs, your game will be exponentially less prone to inconsistency where game mechanics don't complement each other or having redundant controls.
Usually the inputs come in play with many types of basic mechanics such as movements, selections and actions.
Choosing the layouts of controls is sometimes secondary due to the designer decision to work on a core mechanic which executes with just a push of a button. In this case, it works on a plethora of controller devices including a touch screen. Do bare in mind too that some game's mechanics do require specific inputs like motion sensors that a platform supports in which case, the mechanics will have to play according to a specific layout. Unless you can freely design the inputs, think within the constraints.
During the initial stages of a game project especially the prototyping phase, some designers will come up with different ways of play that complements their inspirations. But when the main inspiration of a game designer is about finding different ways of play, everything else becomes a tag on complementary element. Stories will derive from the mechanics to complement it and audio visuals will essentially play the role of relating the mechanics to real world experiences and functions.