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Wikipedia
Generally, the player controls a small number of game characters, usually called a party, and achieves victory by completing a series of quests. Players explore a game world, while solving puzzles and engaging in tactical combat. A key feature of the genre is that characters grow in power and abilities, and characters are typically designed by the player. RPGs rarely challenge a player's physical coordination, with the exception of action role-playing games.
These games usually have a highly developed story and setting, which is divided into a number of quests. Players control one or several characters by issuing commands, which is performed by the character at an effectiveness determined by that character's numeric attributes. These attributes increase each time a character gains a level, and a character's level goes up each time the player accumulates a certain amount of experience.
Do not see where towns, NPCs and non-linearity fall into that definition. And you definitely explore in FFXIII - unless you don't move your character at all in the game and stay where you are.
