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Set in a fictional universe, often (but not always) with fantastic or supernatural elements, alternate worlds, magic and monsters.

An otome game is a story based video game that is targeted towards the female market. Generally one of the goals, besides the main plot goal, is to develop a romantic relationship between the female player character and one of several male or female characters.

http://en.wikipedia.org/wiki/Otome_game

Games with a heavy focus on storytelling and narrative.