The perspective that the Church-Turing hypothesis applies to the physical universe is mainstream but unproven. It is implicit in the work in the original post.
This sounds like the article is claiming that the universe is a computer simulation, or that stuff can't exist if we can't compute it.
Can someone please help me understand why something being able to exist in our universe depends on if we can calculate the physics for it, or where I've gone wrong in getting to this question?
In the Many-Worlds Interpretation, the computing apparatus itself 'grows' exponentially over time.