The paper you reference asks: "Can the theory that reality is a simulation be tested?" That has nothing to do with quantum mechanics, despite the attempt to use the double slit experiment as a component of testing this ridiculous hypothesis*. If we live in a simulation, as I said, there is no particular reason to use elements of quantum theory to "prove" it. See "Last Thursdayism" if you are not already familiar with my explanation.
Quantum theory has many "unusual" elements. What Campbell et al are testing is about as ad hoc as it gets, and certainly far from anything that is going to raise an eyebrow with those familiar with the literature on the subject.
So again, your question has been asked and answered. Read the paper I referenced and you will see that recording is not relevant to the results.
----------------------------------------
*PS On case you think I am being unfairly judgmental: Here is the hypothesis from the paper, which is absurd on the face of it:
"Summing up, to save itself computing work, the system only calculates reality when information becomes available for observation by a player, and to avoid detection by players it maintains a consistent world, but occasionally, conflicts that are unresolvable lead to VR indicators and discontinuities (such as the wave/particle duality). "