It was sometime in the '80s that the question "What is a role playing game?" started to be pontificated on. Since then, of course, it's been non-stop. Every newly published game designer takes their crack at it. Here's just a few bits from some PDFs I have at hand.
D&D Basic Set, Player's Manual, 1983 (Mentzer), page 2 wrote:
This is a role-playing game. That means that you will be like an actor, imagining that you are someone else, and pretending to be that character. You won't need a stage, though, and you won't need costumes or scripts. You only need to imagine.
This game doesn't have a board, because you won't need one. Besides, no board could have all the dungeons, dragons, monsters, and characters you will need!
For now, while you are learning, you will play a role in your imagination. Later, when you play the game with others, you will all be playing different roles and talking together as if you were the characters. It will be easy, but first you need to get ready.
AD&D Player's Handbook, Second Edition, 1989, page 9 wrote:
This is the heart of role-playing. The player adopts the role of a character and then guides that character through an adventure. The player makes decisions, interacts with other characters and players, and eseentially, "pretends" to be his character during the course of the game. That doesn't mean that the player must jump up and down, dash around, and act like his character. It means that whenever the character is called on to do something or make a decision, the player pretends that he is in that situation and chooses an appropriate course of action.
Shadowrun, Second Edition, 1992, page 10 wrote:
(Header "What is a roleplaying game?")
A good question, but not an easy one to answer. Everyone has read a book or seen a movie where the lead character does something that the reader or viewer finds so utterly wrong that he or she wants to yell out and warn them. But whether the reader calls out or not, it makes no difference. No matter what we say, the character will do what the plot demands; we're just along for the ride.
The situation in a roleplaying game is very different. When roleplaying, the players control their characters' actions and respond to the events of the plot. If the player does not want the character to go through the door, the character will not. If the player thinks the character can talk him or herself out of a tight situation rather than resorting to that trusty pistol, he can talk away. The script, or plot, of a roleplaying game is flexible, always changing based on the decisions the players make as characters.
Once CRPGs started to be a widely distributed thing, the statements started to modify a bit. I suspect if Lord British has ever gone on record with a statement, you'd see the start of the fork. Obviously, it took him a few tries to get his mechanical systems down enough that he could actually start exploring the role-play aspect, but he got there, and was one of the earliest to do so.