One thing that seems to be what connects most RPG's is choice; whether its choice in stats, appearance, morality, dialogue, story, background, weapon, there always seems to be at least a few of these in all of the RPG's I have heard of including the old PnP formula. It is why that when these sorts of things are in other games they are known as "RPG features". Exploration, loot collecting and open worlds are not inherent to RPG's, they are features of sandbox games.
This is how I look at it anyway.