I feel like I've drifted into the twilight zone here the past few days.
This is the english language. Words have commonly understood meanings. Combining them creates compound meanings.
Game = a competitive activity involving skill, chance, or endurance on the part of two or more persons who play according to a set of rules, usually for their own amusement or for that of spectators. - OR - an amusement or pastime -- I prefer the first definition when trying to think about "game design"
Board game = A game involving a game board
Roleplaying Game = A game involving roleplaying
Storytelling Game = A game involving storytelling
Adventure Game = A game about adventure
Adventure Roleplaying Game = A roleplaying game about adventure
Adventure Storytelling Game = A storytelling game about adventure
Adventure Board Game = A board game about adventure
If you can take any of those parts out -- Game, Board, Roleplaying, Storytelling, Adventure -- then you could describe that activity without them.
Is Warhammer 40K a Roleplaying Game? No. I can play that game without any Roleplaying.
Is Once Upon a Time a Roleplaying Game? No. I can also play that game without any Roleplaying.
Are all traditional Roleplaying Games actually Adventure Roleplaying Games? No. A Roleplaying game doesn't have to be about Adventure.
Are all Storytelling Games also Roleplaying Games? No. You can have a Storytelling game that requires no Roleplaying.
Are all Roleplaying activities Roleplaying Games? No. You can roleplay without having any competition, rules, goals, challenges, rewards, etc.
If I was the first one to produce a "Wuthering Heights Roleplaying Game" would I have invented that term? No. I might be the first person to use that term, and the first person to make that game, but it's a simple compound word with no special meaning beyond what's contained in the individual words.
So, to review:
If the activity requires Roleplaying... and it's a game... it's a Roleplaying Game.
If it doesn't require any roleplaying, or it's not actually a game... it's NOT a Roleplaying Game.