If you go back to the origins, when did Gygax and friends stop playing 'wargames' and start playing 'role playing games'? When they began adding mechanical distinction between their characters. Me and you are both Fighters, but here's the stats that describe how we're different, and we have different species with quantifiable tradeoffs, and different levels and equipment representing our past experiences. The existence of distinct character description and their harmony with mechanics is at the heart of the thing. This happens to have good synergy with a narrative, but its not required.