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This is way beyond me, but Ethan Siegel provides a lucid rehash of scientific theory in general, and 3 reasons why Wolfram's new 'Fundamental Theory' is not yet anywhere near a scientific theory.

https://www.forbes.com/sites/startswithabang/2020/05/13/3-si...

Wolfram himself never claims that it is anywhere near a scientific theory.

Theory requires a model, but not the other way around. What Wolfram has at present is a model which can be used to represent crude analogues of some things that may exist. It's flexible enough to be able to represent a wide array of different kinds of things, by the nature of being based on graphs (which define their own topologies) and update rules, which re-enact the patterns of positive feedback and complex emergent structures.

Your article asks: "But can he get known physics out of it?" and says not yet.

The OP says he has gotten general relativity out of it, so it appears to be an advance from the state described in your article. I do know enough about the situation to if any of it is valid or anything.

I watched Wolfram present on his new theory when it originally came out in that large expensive book. He sounded like a lunatic. I don't doubt that he is exceptionally intelligent but I am not seeing his stuff being linked up with mainstream physics and that does give one pause.
Reading this does make me feel that Einstein's GR may not be the last word in the mathematical modeling of gravity. (Not to say that this feeling could not be wrong.)