the instructional text on how to apply the rules is every bit as much of a real rule as the number of HP you gain with each level. Thus, I would put the modern role-playing era at about the point when the rules actually told us to start role-playing rather than treating it as a board game.
Gyagx's D&D is not a board game. In a board game there is no fictional positioning. Gygax's D&D is utterly rife with fictional positioning - arguably, that's the bulk of the game, especially in its pre-AD&D versions.
Original D&D was intended as just a game, and the use of "role" in the name is more like the 4E usage as the role you play in the party, rather than the way an actor would use the term. (And we've all heard what Gygax had to say about wannabe play-actors.)
For that reason, I don't consider early D&D to qualify as a real RPG, in the "role-playing" sense of the term. You could certainly role-play within it, if you were so inclined, but that wasn't the point and the rules were not designed to facilitate it. Or at least, there was no indication if that was supposed to be the point, and a very loud voice telling us that it wasn't.
It's not a role-playing game if you're not playing a role
I feel that you are begging the question here - that is to say, you are assuming that the phrase "role playing" has a certain meaning - your preferred one - and then judging all games that call themselves RPGs by reference to that meaning.
I already mentioned, upthread, the example of roleplaying for skills development that law students (and other sorts of students) undertake. That has nothing to do with acting, but is nevertheless truly described as roleplaying. By adopting the role (of an appeals court barrister, or a mediator, or a client, or whatever) the student imposes (i) a limit on permissible "moves" (eg an advocate can't address arguments to his/her opponent, but rather must address them to the court, and that in terms requires adopting appropriate court manners), and (ii) a standard for successful achievement.
Gygax clearly saw RPGing in the same way. By choosing to play a fighter, I (i) limit my permissible moves in the game (eg no spell casting, no use of magical staves), and (ii) set a standard for success (per Gygax's DMG, successfully playing a fighter means displaying leadership and physical courage). The fact that that's not
acting doesn't mean it's not
roleplaying.
That's not to say that one can't bleed into or engender movement towards the other. For instance, some of the constraints on permissible moves that arise by choosing a particular class role are the result of fictional positioning (eg NPCs look to the fighter for leadership because of the way the fighter has ended up being framed within the fiction, and the player of the fighter who wants to keep the NPCs on board therefore finds him-/herself obliged to have his/her PC take the lead). And that naturally pushes players to engage with that fiction, to wonder about why it is that
this particular person ended up becoming a bold warrior rather than (say) a cowardly thief, etc.
But there is no necessity or inevitability about immersion-style RPGing of the sort you favour. It's quite possible to engage with the fiction of, and surrounding, a character without feeling compelled to make choices in the game only from the ingame causal perspective of that PC. The word
causal is especially important here. A player in (say) Burning Wheel who chooses to use metagame points to pump a skill check may well be making choices only from the ingame perspective of his/her PC - s/he is deciding, from that persepctive, to try harder. It's just that s/he is manifesting that, within the mechanics, via a device that does not itself model an ingame causal process.