The rendering loop continues to run. The GUI is immediate mode and is still rendered. In some games visual effects continue to be rendered. If it’s a networked game the network code will continue to run.

Taken from this comment: https://news.ycombinator.com/item?id=47825155

Obviously not every game is doing that level of styling, but often a lot of stuff might still be happening when a game is "paused" for various reasons e.g. aesthetics, or handling input for pause menus, which usually offer you the ability to change all the games settings, e.g. video resolution, volume levels, etc. and also provide you with audio/visual feedback when you make choices, which requires keeping the audio engine running as well as rendering to the screen @ 60 fps.