The choice made by Rose's player about what to do with the gun is a choice to author some fiction - that is what happens when a player declares an action for their PC. (I put to one side approaches to RPGing that I regard as somewhat degenerate, in which it is deemed that only the GM can change the fiction so that players' action declarations for their PCs are treated simply as suggestions to the GM as to how to add to the fiction.) We can see this illustrated in
Step 1 of Vincent's first resolution system, where a player says "I take position on the crest of the hill" and the other player replies "Okay". That is clouds-to-clouds.
The choice to use a trait in Torchbearer is not a choice about authoring some fiction. It is a choice about how to manipulate a resolution process. It has, as its immediate field of operation, not the clouds but the boxes. In this respect it's the same as using a Fate Point to open-end sixes in either Torchbearer or Burning Wheel, the same as using a Call-On trait in Burning Wheel, the same as spending a Plot Point to keep an extra die in Marvel Heroic RP/Cortex+ Heroic. In Vincent's examples, it's analogous to
Step 4 of the third resolution system, which requires a player who wishes to answer to reroll (a player can always opt to open negotiations for consequences instead: In A Wicked Age rulebook p 19). And unsurprisingly that is marked as boxes-to-boxes, with an ensuing leftward arrow (boxes to clouds) at Step 5 as you "say what your character does".
The choice is constrained by the fiction: the established fiction has to be "taken into account" (your phrase) by the In A Wicked Age player, just as it does by Dro when playing Torchbearer. But what is this supposed to show? In Vincent Baker's example of the oppressive heat being the cause of the debuff, the fiction has to be taken into account (presumably no one is going to narrate
oppressive heat as the cause of a debuff suffered by a PC who is trekking across Antarctic plateaus). The use of Call-On trait may have to have regard to the established fiction (eg Graceful can be used as a call-on trait for social skill checks requiring "grace" or "presence" - and that's something that is settled by the state of the fiction, it's not a technical mechanical term). In Marvel Heroic RP, Dr Strange's player can use the Alliterative Invocations ability to spend a plot point to buff certain actions involving magic - this depends upon the fiction in two ways, in that (i) the action has to pertain to magic, which is a matter of fiction and not mechanics, and (ii) (at least as I interpret the ability) the player actually has to have Dr Strange utter the invocation ("By the Seven Rings of Raggador", etc). That doesn't change the fact that, in all these cases, the decision to use the ability is still a decision to manipulate the cues (boxes) in a certain way.
I am saying that Dro deciding to break a tie is not the same as taking the high ground granting +2 to hit, nor as shattering the faceplate of a character on the surface of Pluto causing that person to begin freezing, suffocating and decompressing. In both those cases, we have a relationship of entailment.
In the first, we have one bit of fiction (taking the high ground)
entailing a mechanical state of affairs (gaining +2 a +2 to hit): the arrow in
Step 3 of Vincent's first resolution system does not reflect a
choice made by a participant, but a
requirement that follows from the game's rules.
In the second case, we have one bit of fiction (
I'm on the surface of Pluto and the faceplate of my space helmet has been shattered) entailing another bit of fiction (
I'm freezing, suffocating and decompressing). Depending on the RPG being played, that second bit of fiction might also entail something mechanical (eg in my Classic Traveller rules I make it 1D of wounds, +1D per 15 seconds until dead).
These are the rightward pointing arrows that Vincent notes are missing from In A Wicked Age, and that make a moment of RPG resolution
fiction first. They are present in AW and DW, captured by the slogan "If you do it, you do it." There are aspects of Torchbearer that exhibit this structure - for instance, when Dro decides to have Harguld hold of the Gnolls by shooting at them with a crossbow, that establishes the need for a Fighter check.
That's fiction first!
We can also compare the use of a trait to break a tie to the Burning Wheel rules. In BW versus tests, a tie actually represents something in the fiction, namely, the opponents having fought to a standstill. On p 275 of the Adventure Burner (reproduced on pp 142-43 of The Codex), are the following two examples:
Two wrestlers attempt to best each other with their skill. They tie. They cannot overcome each other with technique, so they surge back into the fight and attempt to overpower their opponent - Power tests. This too results in a tie. They are matched in skill and power, so now it's a matter of endurance - Forte tests. Who can outlast the other? . . .
Two characters rush for the sword. They tie on a Speed test. They get there at the same time. They both grab for the sword. They tie on an Agility test. They both grab it at the same time. The attempt to wrestle it out of each other's hands. the test Power and . . .
It's an effective technique . . . It does require the GM to be nimble and ready with lightning-quick complications and descriptions so the players stay tightly focused on this immediate, pernicious problem.
We can see how the tie is not just a mechanical state of affairs, but a state of affairs in the fiction (ie there is a leftward arrow, from boxes to clouds) which the GM has to narrate (with "lightning-quick" complications and descriptions) that then demands a new action declaration from the player(s) (like "I try to wrestle the sword from her hands!") which then generates a rightward arrow just the same as the rightward arrow that led to Dro testing Fighter to try and hold off the Gnolls.
It's obvious that breaking a tie by spending a trait check is nothing like this.