Wittgenstein argued in his Philosophical Investigations that there is no single feature shared universally by all games, but rather that all games share what might be called 'resemblances'. For much of the long history of language, 'game' has enjoyed and participated in various degrees of vagueness.
"Role-playing" also participates in vagueness; it seems to follow naturally from the fact that two nebulous terms, "role-playing" and "game", taken together, are not going to admit of convenient or simple understanding - this admission does not of course preclude "RPG" from being used however the term is perceived to best serve marketing, or for that matter, any other interest(s).