In the quote upthread from Men & Magic, we see "Before they begin, players must decide what role they will play in the campaign, humans or otherwise, fighter, cleric, or magic-user."
This is echoed in Gygax's PHB, where (p 18) it says that "The approach you wish to take to the game, how you believe you can most successfully meet the challenges which it poses, and which role you desire to play are dictated by character class (or multi-class)."
I think these passages make it pretty clear that the core of the "role" in
roleplaying is functional - what
abilities does the player's character enjoy, in the fiction? The character
goals are all taken to be the same, namely, acquiring loot such that the player can gain levels by earning XP. This is why we see, in the PHB (p 106), the following:
Experience is the measure of a character's ability in his or her chosen profession, the character's class. . . .
Gaining experience points through the acquisition of gold pieces and by slaying monsters might be questioned by some individuals as non-representative of how an actual character would become more able in his or her class. Admittedly, this is so . . . This is a game, however, a fantasy game, and suspension of disbelief is required. . . . While praying and religious-oriented acts are more properly the activities for which a cleric would gain experience points, this is not the stuff of exciting swords & sorcery adventure. So too, fighters need physical training and weapons practice, magic-users long hours of study in tomes of arcane lore, and thieves the repetition of their manual skills and discernitory prowess; but none of this is suitable to gaming. It is, therefore, discarded and subsumed as taking place on a character's "off hours".
The DMG (p 86) similarly says that
Players who bolk at equating gold pieces to experience points should be gently but firmly reminded that in a game certain compromises must be made. While it is more "realistic" for clerics to study holy writings, pray, chant, practice self-discipline, etc. to gain experience, it would not make a playable game roll along. Similarly, fighters should be exercising, riding, smiting pelts, tilting at the lists, and engaging in weapons practice of various sorts to gain real expertise (experience); magic-users should be deciphering old scrolls, searching ancient tomes, experimenting alchemically, and so forth; while thieves should spend their off-hours honing their skills, "casing" various buildings, watching potential victims, and carefully planning their next "job". All very realistic but conducive to non-game boredom!
Of course, and somewhat contra Gygax, it is possible to make a FRPG that has a significant place for activities like clerics praying and engaging in ritual, fighters tilting and riding, MUs engaging in magical experimentation, and thieves casing buildings and planning their jobs. Burning Wheel provides an example. But Gygax's real point in these passages, at least it seems to me, is that in
his (and Arneson's) game, the goal of play is gaining XP, and the development of the player character by earning XP from gold is part of the feedback to and reward gained by the player, and hence we ignore the "realistic" stuff he describes.
And in
his (and Arneson's) game, the character - defined primarily by class and secondarily by race - is the role that is adopted to pursue that goal. This is reinforced by PHB p 106, which first sets out the major aims of each character class,
clerics' major aims are to use their spell abilities to aid during any given encounter, fighters aim to engage in combat, magic-users aim to cast spells, thieves aim to make gain by stealth, and monks aim to use their unusual talents to come to successful ends
.
and then says,
If characters gain treasure by pursuit of their major aims, then they are generally entitled to a full share of earned experience points awarded by the DM.
The goal of play - treasure acquisition - is clearly defined; and the major aims of each class - the "role" - are the means that each player adopts to pursuing that goal.
The idea of class-as-role, establishing "major aims" or means whereby a player obtains treasure, is further reinforced by the discussion of rating play in the DMG, p 86:
Consider the natural functions of each class of character. . . . Briefly assess the performance of each character after an adventure. Did he or she perform basically in the character of his or her class? . . . Clerics who refuse to help and heal or do not remain faithful to their deity,
fighters who hang bock from combat or attempt to steal, or fail to boldly lead, magic-users who seek to engage in melee or ignore magic items they could employ in crucial situations, thieves who boldly engage in frontal attacks or refrain from acquisition of an extra bit of treasure when the opportunity presents itself, "cautious" characters who do not pull their own weight - these are all clear examples of a POOR rating.
The fit between the PHB description of class roles, and of the DMG description of failures to perform those roles, is clear.
The only personality-type idea that figures in the account of role given by Gygax is alignment. We see this in the quoted passage from Men & Magic (about it being "necessary to determine what stance the character will take"); and again in the DMG p 86 discussion of rating players, where - in addition to the class role points that I've quoted just above - Gygax says that the GM must
Consider also the professed alignment of each character. Briefly assess the performance of each character after an adventure. . . . Were his or her actions in keeping with his or her professed alignment?
None of the above is to deny the point that, in reality, many D&Ders (thought as
@AbdulAlhazred points out, not necessarily all of them) started playing their characters more elaborately. And Gygax himself tips his hat to this point in the intro to his PHB, where (p 7) he writes that "Each of you will become an artful thespian as time goes by", although the same sentence goes on immediately to set out the goal of play: "and you will acquire gold, magic items, and great renown". Classic D&D, as presented by Gygax in his rulebooks (and in Moldvay's version of it), will need pretty extensive supplementation to be played with the goal being something other than the acquisition of treasure from dungeons and the like. The original OA provides an example of what such supplementation might look like (including variant XP rules for some classes), although I think it's still fair to say that the game OA presents is a bit incoherent. Another obvious supplementation, well-known in discussions of high-level classic D&D play, is the addition of genuine wargame rules so that the game shifts from dungeon/hex-crawling to domain management and conquest.
I've played freeform sessions and relatively free-form miniature scenarios where every character has a goal (analogous to your short page of character notes).
I've also seen classic D&D's character and resolution mechanics used for this sort of scenario - eg Lewis Pulsipher's Bar Room Brawl, D&D-style in an early White Dwarf. But these require the sort of supplementation I've described above: writing character goals; setting up possible victory conditions; etc.
This is not essential to, or inherent in, the Arneson-Gygax game.