You’re a learning game designer, looking for ways to explain the basic ideas behind your ideas to stakeholders. You need “greatest hits” theory that’s simple enough to explain to anyone.

Here’s Wolfram‘s great diagram and explanation of the components of a game:

Wolfgang’s 4-layer cake of game design

It obviously doesn’t describe ALL designs, but it’s a great starting points.
http://www.funstormgames.com/blog/2012/06/designing-around-a-core-mechanic/