I am presently reading The Elusive Shift by gaming historian Jon Peterson, author of Playing at the World, which explores exactly this question: what did the early players of D&D and related games, according to their own writings in fanzines and such, consider ”role-playing” to mean, and when was the transition point from “a funny kind of war game” to a new genre of recreation? The quoted fanzine discussions are not unlike those we still have now online. There was a lot of back-and-forth about playing to your ability scores and alignment even when that was suboptimal, vs. playing yourself doing dungeon problem-solving.
Further, Peterson finds antecedents of D&D’s style in wargames (including Mike Carr’s Fight in the Skies, later published by TSR as Dawn Patrol) that encouraged players to increase their engagement by making up personalities for pilots and even individual miniature soldiers, and having them react according to those personalities rather than just according to optimal tactics from the player’s POV.
This is much where I was going to go.
Playing at the World covers this a bit, but my understanding is that the Elusive Shift digs more into the conversation and the discussion between the major groups of early roleplayers, coming primarily from the sci-fi fandom and wargaming traditions, to define what roleplaying is.
Essentially it comes down to playing a role, but you can do that without
acting.
I think in the 70s the approaches were more localized and groups varied more. The distinction between groups which mostly employed what some people call "pawn stance", where your character is essentially a game piece whose personality, if any, is minimal, vs. "actor stance", where you do your best to embody a distinct character with personality clearly separate from your own, was more clear. AD&D and those early modules like Keep on the Borderlands and The Village of Hommlet (both published in 1979, like the 1E DMG) started to cater more to this actor tendency and the idea of embodying a specific character as a more complete or advanced form of play, whereas OD&D had been quite vague about it, and the Basic sets which followed, as we saw with that paragraph equating role with class, didn't talk as much about embodying someone like Falstaff the Fighter.
Once people started participating in larger conversations about gaming, whether in AP fanzines, the letters pages of Dragon or other magazines, at conventions, or later, on the internet, we got to see more debates about what roleplaying was or should be.
As I recall it was around 1983 that Sandy Peterson and others came up with the humorous four types of roleplayers- the Real Men, Real Roleplayers, Munchkins and Loonies, lampooning major player tendencies, but also illustrating how some players were already deeply into getting their PCs into "love affairs and death feuds", so clearly this was a strong and well known contingent by then (the below-linked doc was compiled in the 90s, though, after some years of discussion and expansion, but I believe sizable chunks of it date back to the early 80s):
I think by the time we get into the 80s, though, the idea of embodying a character and acting in that role, optionally with funny voices and accents and so forth, was very well and widely known and largely held up as the model form. In addition to Gary's words quoted above, you get into what some folks call the Hickman revolution when TSR started to lean more into longer narratives in games, and then the explosion of D&D novels starting with the first Dragonlance book in 1984. A new player reading Dragons of Autumn Twilight, or The Crystal Shard a few years later, would likely see emulating these heroes and their in-character voices and dialogue as goals and forms to emulate. Although if they had a regular play group, that culture would be the primary influence.