The passage I quoted doesn't explicitly say "hey, just so someone who comes along 40 years from now doesn't get confused, I want to clarify that I'm talking about the personalities, not just the raw statistics, of these characters".
Okay, so that's a "no".
Now reread Gygax's discussion of playing the game ("successful adventuring"), as he calls it, on the closing pages of his PHB (before the Appendices). He talks about choosing equipment, memorising the right spells (with no suggestion that spell selection might reflect personality), the right balance of capabilities (including magic items), etc. In your words, the characters are "pawns".
If you're just "fulfilling a function" within your group, you are still interacting as Jim, Bob, and Mary who work at the office together. You're just modern people playing a game. The characters don't actually participate in this, and are not the ones interacting; the players are interacting, the characters are just the pawns.
The players inhabit their characters in the shared fiction. This is the difference from a board game. In order to understand your "permissible moves", you have to think yourself into the fictional situation, which includes your fictional positioning vis-a-vis the other characters.
This is why the emergence of PC personalities is a natural byproduct of playing the game even in the Gygaxian approach - it's not as if rhe change in conceptions of roleplaying between the mid-to-late 70s and the late 80s/early 90s came from nowhere!
But look at (just as one example) this exchange in Gygax's example of play in his DMG (pp 99-100):
LC [= Leader Character]: "Let's change the plan a bit. The cleric and I will hoist the gnome up and hold his legs firmly while he checks around for some way to open the secret door. Meanwhile, the halfling and the magic-user will guard the entrance so that we won't be attacked by surprise by some monster while thus engaged."
. . .
OC [= Other Character] (the gnome): "Then I'll see if I can move any of the stone knobs and see if they operate a secret door! I'll push, pull, twist, turn, slide, or otherwise attempt to trigger the thing if possible."
DM: "The fist-sized projection moves inwards and there is a grinding sound, and a 10' X 10' section of the wall, 10' above the floor in the center part, swings inwards to the right."
OC: (The gnome) "I'l pull myself up into the passage revealed, and then I'll see if I can drive in a spike and secure my rope to it, so I can throw the free end down to the others."
DM: . . . "You see a sickly gray arm strike the gnome as he's working on the spike, the gnome utters a muffled cry, and then a shadowy form drags him out of sight. What are you others going to do?"
LC: "Ready weapons and missiles, the magic-user her magic-missile spell, and watch the opening."
Here we see the players interacting as their characters, inhabiting the fictional situation and relating to one another in that manner. But there is
not the least hint that establishing an interesting and entertaining personality (as the 2nd ed AD&D PHB talks about) is relevant to the game. Searching for an opening the secret door is an
operational problem, not a dramatic one; and the attack upon the gnome creates a
tactical problem, not an emotional one.
the primary level of interaction is in terms of these fictional persons and their stories, not in terms of the numbers used to do the thing.
Of coures the primary level of interaction is in terms of these fictional persons! That's the difference from a board game. But that doesn't mean that distinctive, entertaining personalities are relevant. Just look at the example of play in the DMG. Look at Gygax's advice on how to play the game in his PHB.
Or look at the quote from MAR Barker, not far upthread. The "stories" of these persons are envisaged as being stories of gaining power by exploring and looting dungeons. When they talk about challenges to be faced, they are clearly envisaging tactical and operational challenge, not emotional or dramatic challenges.
Are you saying that you can't comprehend anything which could ever exist which would be "portraying a character" rather than "fulfilling a function", or are you saying that you can't see why anyone would think that D&D's "role playing" is closer to the former than to the latter?
Neither. I'm saying that there are different ways of thinking about roleplaying (in D&D and other RPGs), and that not all of them invole "portraying a character" by conceiving of and then acting out a distinct, entertaining personality.
I am also saying that we can see these different ways expressed in different D&D books. Gygax's PHB, Moldvay Basic and Empire of the Petal Throne (which for current purposes can be safely treated as a D&D variant) all present roleplaying in terms of taking on a certain set of functions and capabilities and deploying them to meet the challenges of the game. Whereas the 2nd ed PHB says that roleplaying means coming up with a
unique and entertaining personality.
Those early texts present the
goal of roleplaying - what Gygax calls "successful adventuring" - as extracting loot from a dungeon so as to earn XP and thereby go up levels. The 2nd ed PHB presents the goal as being to have fun acting out your PC's personality and reacting to how other players act out theirs.
I have a nice simple example from a recentish game. Epic-level pathfinder. We're fighting epic-level people. One of them has a sword which is probably worth more than everything our party owns put together. And he is a total jerk, and he waits until the last minute, then holds the sword out and offers his surrender to the lawful-good dwarf. The dwarf is really really mad at the guy.
Turn comes up...
Bill: I take my full round of attacks on his sword.
Now, the thing is, Bill's got an adamantine weapon. He will destroy that sword. This will cost us more money than we, as a party, have ever seen all put together. It's worth significantly more than the full-sized magical ship we're capturing. This is an atrociously bad idea in terms of "fulfilling a role within the party". But it is absolutely, unambiguously, in-character and correct for Kal to do that. Bill did it, not because it was a good choice in terms of the party's goals, but because it was what Kal would do.
And in the 40+ years I've been playing D&D, outside of your threads on this forum, I've never actually seen anyone use "role-playing" to refer to anything other than "trying to play the character true to their personality and nature".
Roblin Laws has a similar discussion, I think in Over the Edge, where he refers to the birth of roleplaying (in your preferred sense) as occurring "The fist time someone took a sub-optimal action because 'that's what my guy would do'." (I don't have the book with me, so I'm paraphrasing, but I hope not too loosely.)
This doesn't mean that that's the only way of thinking about roleplaying, though. As I've said, literally
nothing in those early rulebooks suggests that this is an important part of playing a character. And Laws himself, in his Dying Earth RPG, has written a RPG where creating a unique and interesting personality is expressly stated not to be an important part of playing the game. The reason for this, as explained in the rulebook, is that most people in The Dying Earth stories have more-or-less the same peronality and motivation (basically greedy, self-serving, etc but not unutterably ruthless).
I think it's not a coincidence that there is a similar non-emphasis on personality in The Dying Earth RPG and Gygaxian D&D, given the influence of Vance on Gygax's conception of the fantasy world. I also think it's why Vincent Baker, when he set out to run Lamentations of the Flame Princess (an OSR game) found that
"the only way for me to reconcile my expectations with the reality of the rules was to go all frickin' Vance with it. The moral underpinning has to go out the window, to be replaced by an ironic and cynical relativism".
As I've been posting in this thread, I think that one way of trying to understand indie-style games is that they want to use the functional/capabilities approach to produce something other than Vance, and so they change what counts as a character's functions/capabilities/responsibilities.