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

An inclusive term that describes relationship-focused Visual Novels and Interactive Fiction games that feature a wide range of diversity such as racial, religious, and LGBTQA+ as well as more

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

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