There is a really easy, and obvious litmus test for RPGs that no one ever uses for some reason. Role playing games explain their very heart and soul in the genre title. Any game that the story is essential to the game would end up as a RPG. It works extremely well and only occasionally leaves you with a vague answer.
Examples Starcraft 2 certainly seems very story driven. However if you remove all story dialogue you have a game that would not be worse off on a fundamental level. The game play is strong enough, and clearly been focused on to such an extent that the story is secondary at best. Any and every fighting game follows the same pattern.
I just don't get all these other definitions. What does stat growth have to do with role playing? Many tabletops (the source of many if not all original video game RPGs) often had zero stat growth with leveling. What does turn based combat have to do with role playing? Another legacy from the probably source material that stems from everyone yelling "attackattackattack" at the top of their lungs is no fun for anyone. Following the story of the character, and guiding his actions at your whim (assuming his role, or playing it if you will) is the only logical necessity for a RPG.
