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Visual novels are interactive stories. They focus mainly on character development and plot rather than action and gameplay mechanics.

Games with a woman as the main character.

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

Either prominently containing or entirely themed around romance, this genre is typically focused on interpersonal romantic relationships between characters and the player.