with the same success the study refutes the researchers' religious belief in the truth
I would imagine the hand-wavey response might not be far away from "God is not algorithmic".
The concept of "god" and "simulated universe" seem to be essentially the same
I'm an atheist, but I can tell you that no, they are not - at least not to many believers.
From the perspective of empirical analysis—how?
I'd say the question is flawed (at least, in this context); religion is purposefully the opposite of empiricism for most everyone I know, anecdotally. Hence why it's given the term "faith".
Exactly. How do you formulate "simulation" without such faith? The idea of demonstrating evidence of either god or simulation is equally nonsensical. The people grasping for such might as well grasp for the spaghetti monster.
I agree with you, don't get me wrong. I'm just pointing out that comparing the two as if disproving an inherently empirical thing (we're in a simulation) also disproves a belief-system/faith-based thing (God or religion) is nonsensical in that the second isn't rooted in empiricism, algorithms, nor the scientific method. They don't believe God is something to be proven or disproven, he just is and that's that (as per their faith).