All fundamental theoretical physics starts by building a model idea and exploring what the possible consequences are in a mathematical way.
The goal is to model the real world, but it's far too difficult to go straight from a fundamental model up to the world observations to find out if the model works.
Doing that "work out the consequences" work can take decades, and a lot of people.
So models are built, explored, their consequences worked out, and if they match something interesting in other more well-established theories, then the models are looked at with more interest and developed further. If not, the models are tweaked or thrown away.
You could call it a branch of mathematics, but in a sense all theoretical physics starts out that way, so we just call it theoretical physics when the goal is to model observed reality while providing a useful underlying model.
Browse the papers on arXiv.org or any theoretical physics journal and there's a lot of exploratory model-building like this. It's very common.
Graph-space models are also not unique to Stephen Wolfram. Several physicists (paid ones) are exploring these models as an approach to reconciling relativity and quantum physics. In a sense, this is what deriving from observation looks like: We've observed relativity and quantum, and we still haven't figured out how to understand the logical consequences of both together, so exploring theoretical underlying models like this is necessary to understand current observations.
The article's theory is not "philosophical" or "metaphysical" theory where nothing can be tested in principle. He explicitly talks about measurable effects differing from other models, albeit with many difficulties and potential intractibility due to computational limits.
But the point is there are, in principle, observable differences, making it more than just a metaphysical model, and if it's intractable to access them we can't figure that out without studying the model further. Even if we can't, there not being able to may have consequences as well (like the way the Heisenberg uncertainty principle turns out to have logical consequences, not just preventing measurements).