"Though important, I think this isn't quite right because it doesn't make a distinction between a role-playing campaign and a war-gaming campaign. There's another step to be taken here, and I'm not really sure what it is."I'm assuming here he's talking about multiple sessions of a role-playing game with the same characters vs. multiple sessions of a war game with continuing individual warriors or generals. He's right in that mere continuity, which a multi-session war game has, can approach a role-playing game, but there's still something missing that makes a role-playing game different. I'd argue that the missing element is ... continuity.
The way I see it, there's two kinds of continuity: the continuity between battles (or puzzles and situations, in a dungeon, or sessions, in multi-session Monopoly,) and the continuity within a battle (situation, session.) A military campaign with multiple battles and a focus on individuals has the former kind of continuity: the same warriors can fight in multiple battles, and may even have non-combat events that occur between battles. But what makes a role-playing game different is that the player can opt to take completely unanticipated non-combat actions in the middle of a conflict.
War games sometimes include rules for things like mercenaries stopping to loot or recover fallen comrades instead of fight, but an RPG allows any conceivable action to occur in the middle of combat, and allows the action to affect combat or persist outside of the conflict. The players may attempt to bluff the enemy, or throw sand in their eyes and run, or jump in the chasm that was meant as an obstacle, or many other actions. And the players may bear a grudge against the one character who stopped fighting, grabbed the biggest diamond, and ran.
The broader form of continuity between battles helps distinguish a character as a personality. The narrower form of continuity within a battle helps distinguish the world the character exists in as being a real place, with a series of events that exist as more than a mere result of game mechanics.
This is why I included a rule for improvised actions when I talked about converting Monopoly into a role-playing game. In my mind, improvised actions are a necessity, if you want continuity at every possible level.