Yeah, I'm not really saying EITHER of those things. RPGs are not all fundamentally the same, EXCEPT (and here Vince and I agree IMHO) they must involve an interaction between fiction and mechanics/state in which both MATTER (IE different fiction or different state would result in a different outcome and thus differences in following fiction, etc.). Beyond that @pemerton enumerated a few possible 'Processes of Play' as I call them, or distinct STYLES of process of play. There are deep differences between games using different ones. Likewise when discussing what Vince is calling 'exceptionalism', I don't think he is meaning to say that RPGs are JUST LIKE other kinds of games. He's saying they ARE games, and thus what we understand about games in general applies to RPGs. Nothing I am saying is in contravention to either of those positions, as I understand them.Can I ask you to reread what I wrote? I am speaking there of a relating or retelling: the game process yielding a linear narrative. I point that out in order to get at the exact "fiction" that the OP is concerned with, which I believe is closer to the "fictional positioning" that VB describes as "a feature that some games have and others don't". It is that latter technical feature - fictional positioning - that I think your discussion of arrows rightly relates to.
Vincent opens that blog post with
He goes on to point out that many features that might be thought to be unique to roleplaying (making them putatively exceptional) are found in other games. However, he is comfortable saying that fictional positioning is a distinct technical feature of RPG. I'm saying that "fiction" in the common sense of a linear narrative yielded by some process, is not unique (among games) to RPG. But only as I say, to better get at the OP's theory.
EDIT And note here some consequences of Vincent's opening sentences. RPGs are fundamentally games. Different RPGs are different games.
As I said before, in reference to fiction and games in general, it may well be an interesting area of study "the fiction of games." I personally am not that interested in it when it doesn't integrate with play (IE when it is definitionally not an RPG). Anyway, the upshot is that we can say "these games are board games" and "this games are card games" and we can say "these games are RPGs" and I think there are fairly clear cut ways to decide how to apply those labels. That doesn't mean we should focus EXCLUSIVELY on those labels, card games and board games surely share elements, and so do RPGs.