The definition of a game engine is that its a programme code which controls the structure and mechanics of the game. Without it then theres no game.
Game engines can be reused again for sources of inspiration. An existing game engine can empower your own ideas and can be a great starting point. Not every game needs to be started from scratch, it can be developed by an already existing game engine. It's an unseen code that drives the visual action on screen. Obviously they are rules to different games how their characters behave. So using an existing game engine you can then replace the visual aspects and model data to create the new one which is different. Reusing existing game engines is also very financial, meaning companies save money rather than splashing out on a whole new game engine.
Creating a game engine from scratch takes a long time and very problematic for programmers to remove bugs in the code, and mentioned before, very pricey. It may seem simple but no matter how you look at it everything comes at a price. When using an existing game engine you have to pay for a license and the company your using the game engine from.