As far as I can tell, the article says nothing about category theory and doesn't claim to. It's a popularization of recent probabilistic investigations in numbe

As far as I can tell, the article says nothing about category theory and doesn't claim to. It's a popularization of recent probabilistic investigations in number theory, popularization of math is what Quanta does. When it says "Mathematicians are taking ideas developed to study random numbers and applying them to a broad range of categories" I'm pretty sure it means category in the non-technical sense, category as in classifying into categories. The term doesn't appear again in the article.