A chess set is designed to play chess. The game and the stuff are tightly tied to each other. Uno is a card game that uses a specific deck. A standard deck of cards can be used to play a lot of different games. New games can be made by making rules around that common deck of cards, like numbers go on the same number, or black goes on red.

The very first games were like chess games. To input controls and output the game state they had to write it from scratch because it didn't exist yet, both for text-based games and graphical games. Eventually instead of rewriting the entire game from scratch every time, developers made flexible systems that could take the parts that make their game unique and reuse common elements, like taking and interpreting input, managing the state of the game, etc.

Game engines are also used in text adventure games. You tell it what rooms there are, how they're connected, what objects are there, and what you can do with them.

As you get more complex and graphical, you start adding animations, images, sound, physics, and so forth.