The core of a games functionalities, meaning, the software, that handles player's inputs, creating graphics, communication via network, physics calculations, is called the engine of the game. An engine is not yet an entire game, but it is a necessary foundation of a game. Unless a game is written without well defines layers within its architecture, there is usually at least the engine itself, on which a game layer is based. That means, artwork, game mechanics and similar aspects must be supported by the engine, but are not (necessarily) created by the engine itself.
Some engines are rather versatile, e.g. the Unity engine can be used for a majority of games, as it is not specialized to a specific genre. But that on the other hand requires a lot of work to be invested to actually get a game based on it, going, as e.g. skripts and assets that make the actual game mechanics will have to be designed first. Other games have a more specific engine as a base, e.g. the Unreal Engine 2, which is mostly used for shooter-like games.
As an example the Storm3D engine as used in pure RTS titles, such as Star Trek: Armada, but also in a mixed action Shooter-RTS, like Battlezone 98 Redux.
See also List of Game Engines.