::sigh::
Luke (and Daniel) is using a very specific definition of Simulationism that applies to game design, as one of three Creative Agendas, one small element of the Big Model.

Originally Posted by
The Big Model
Commitment to the imagined events of play, specifically their in-game causes and pre-established thematic elements. One of the three currently-recognized Creative Agendas. As a top priority for role-playing, the defining feature of Simulationist play. See Simulationism: the Right to Dream.
If you really want to go down the rabbit hole, you can read a whole essay on it.
To get really technical, creative agendas don't really apply to games. They instead apply to the aggregate aesthetic priorities of a group of players. However, we accept that certain games do facilitate certain creative agendas better than others.
However, rather than getting into all of that, we can boil the thought on creative agenda down to a handful of ideas:
1. Different people get fun from role playing games in different ways.
2. There are at least three readily identifiable priorities for getting fun in RPGs: the challenge of the game (i.e., gamism), addressing the premise/theme (narrativism), and experiencing the world/setting/story/character with versimilitude (simulationism).
3. Assuming your group is functional, you're going to naturally put one of those priorities ahead of the others. By which I mean that when two or more elements come into conflict, the most satisfying outcome for your group will be an outcome that preferences your priority.
With that in mind, consider what it is that Burning Wheel preferences. I'll give you a hint: It's not about making it feel just like that story you just read. It's not about experiencing the psychological processes of your character. It's not about making sure that the setting has verisimilitude.
All those things may happen in the course of play. But what it all comes down to--what every rule and process in Burning Wheel exists to do, whether you see it or not--is to ask the question: "Do you really believe that?"
The moment you say, "fuck it, I don't care what happens, it's a Belief," or "I know it's a Belief, but that obstacle is too high!" or "He did what?! Fuck him. I'm changing this Belief!" Well, then you are addressing premise.
I corner him and stab him in the face!