Time based games
Life-simulators and similar dating-simulator games often include tracking of periods within each day where certain options are available to the player. For example, they can work on week-days between 9am and 5pm to earn money. At night they can go to a bar, gym, or nightclub. At the weekend they could visit the beach or a park.
The player has to balance their cash and often energy to complete the tasks they choose to do.
Like map-based games the story structure is not present in the basic structure of the game. It must instead by handled by the code making various events and encounters possible when pre-conditions have been met. This makes the style harder to envision for those coming to development from an author background.
Map and time elements are often present in the same game. Where this is the case the time element is usually the more important one as it informs or may force changes of location.
And then there are games that involve time travel and potential temporal paradoxes...