The big difference between an RPG and any one of those other story-telling methods is that an RPG demonstrates internal causality. The reason we care about what happens in the story is that the outcome follows impartially from the mechanical processes which represent the narrative, rather than the players manipulating the story directly.
This might be why
you care about what happens in an RPG. I know it doesn't universalise among RPGers, though, because it is not true of me!
(It also gives rise to a puzzle: what is the point of the players? Why can't their place be taken by some sort of mechanistic decision-making process?)
Players attempt to strike an enemy in the hopes of it dying
Well, at my table they roll dice. The only striking taking place is in the fiction -
imaginary striking.
Players don't choose for an enemy to die, and then roll to see if they have enough narrative control to make it happen.
<snip>
the attempt is the extent of player influence. Upon making the attack roll, they've already succeeded in shaping the fiction to the maximum extent that it is possible for a player to shape the fiction.
Everything that happens after the attack roll, whether or not that includes the enemy dying, is out of the player's hands in the same way it is out of their character's hands.
Players declare actions for their PC - say, an attempt to kill an enemy - and then engage the mechanics to see what happens. The mechanics tell us what results from the declared action. The roll is not to see if the player has enough narrative control - it's the working out of the device for control over the narrative.
The fact that everything that happens after the attack roll seems orthogonal to the question of whether or not it is the function of the mechanic to settle the content of the fiction. You can settle the content of a fiction in advance: eg We're writing a story together, and it's got to a cliffhanger bit. We're not sure whether or not the protagonist should live, or whether the protagonist should die and the plot should switch to an investigation of the death (say, like Psycho). I say "We'll toss a coin - heads the protagonist lives, otherwise curtains!" You agree, and toss the coin. At that point, as the coin spins through the air, the content of the fiction is outside either of our control; but that doesn't mean the flipping of the coin doesn't serve the purpose of establishing the content of the fiction.
Now, suppose the two of us disagree over the way the story should go - I want survival, you want curtains. We could easily establish a bidding system, where each of us gets a certain number of points to bid (say, 100 for the whole story) and that means that whoever cares the most at one particular juncture gets his/her way.
PC building resembles this. It's establishing the contexts in which a players' desires for the fiction will be more likely to come true. Eg if I put a high score in swordfighting, then when my character is swordfighting my action declarations are more likely to succeed - which is to say, my desires for the direction of the shared fiction are more likely to be realised.
In the fiction, this might be because my guy is a skilled swordfighter, or because my guy is a plucky hero with a big heart who happens to carry a sword - that will depend on the details of the system in question.
cubes are a subset of clouds which happen to be quantifiable
No. Cubes are things in the real world; clouds are imaginary things. The former are not a subset of the latter.
if your goal is to save the world by throwing the ring into the volcano, then success in doing so is still meaningful even if it involves erasing the ring from your character sheet.
Vincent Baker doesn't say much about "aide-memoires" for the fiction - eg notes about who loves whom, or what is north of where, etc. (Eg when you knock my character down, I might make a not of that so I don't forget.)
Is the equipment list merely a reminder of the fiction, or a mechanical constraint? I think different tables probably take different approaches, although in Torchbearer, and at least some takes on classic D&D, it's a mechanical constraint - a cube.