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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

Focused on an interpersonal relationship or set of relationships between characters (and frequently, the player).

Games with a heavy focus on storytelling and narrative.