e) Renderer / Engine Core
In game engine, engine core / renderer consist of have some sub categories which is: Visibility, Collision detector, and Response, Camera, Static Geometry, Dynamic Geometry, Particle Systems, Billboarding, Meshes, Skybox, Lighting, Fogging, Vertex Shading, and Output.
f) Game Interface
The game interface itself is a layers between game engine and the game itself. The Game Interface function is as a control with purpose to give an interface when inside the game engine's have a functions with dynamic characteristic, so t could make game development much easier.
g) The Game
The Game is the core of the use of the game engine itself, so its up to us to develop The Game.