I am not sure if I am missing any core concepts as I am making my games. But here are the general things the games I have written has taught me thus far:
1) Implementing a main loop
2) Implementing a game loop
3) Keeping track of the state of the object
4) Collision Detection
5) Keeping track of the state of the game(Main Menu, GameOver, Victory, Gameplay)
6) Animation Algorithms
7) Textparsing and then drawing the appropriate art asset corresponding to the numeric or letter text data.
Any more concepts I should know?