I guess one of the most fundamental difference between Wolfram’s model for fundamental physics and traditional physics is that Wolfram’s doesn’t have the concept of measure or of continuum at the fundamental level. Space and time, according to Wolfram’s model of the universe, are emerging properties of ‘the network’. Without such things as space and measures, there is no numbers in the fundamental “equations” that drive the system.
While I am not a big fan of Wolfram’s physics (I think it’s a bit backwards that he took something that he knows very well and somehow finds that it’s how the universe works), I kind of like the idea that space and time emerge from something more computational.
I think that’s what the article should have been focused on...