The term "role-playing" suffers from meaning very different things to different people. On the one side very simple hack'n'slash games like Torchlight (only €4 on Steam this weekend) are generally called role-playing games, on the other side some people insist that only by speaking fake Elizabethean English in character can you really roleplay. That there is a clash of definitions can be seen in the fact that MMORPGs have RP servers, which implies that on the other servers no role-playing happens although we are in a role-playing game.
That old discussion flared up again this year when Mass Effect 2 came out, and did away with some staples of RPGs, for example the inventory. So people discussed whether ME2 was still a RPG or not. Reader Phantasmagoria sent me an interesting link to Blog of War, where GarethF reduces the definition to: "‘RPG’ is a communication shorthand term for a game which shares common features with the other games classified as ‘RPGs’.", but then presents his case very sensibly. Worth reading.