This article is spot on, and some of the behaviors really do seem more indicative of "mathematical people" -- which I suggest really stands for "those who have done research in a 'mathematical' field." (The key being the mix of cold, hard precision in the idealized proof with the squishy, intuitive, human activity of discovering what is pretty and true -- an aspect usually lost in math education!)
Some examples I found most poignant:
- The article mentions "fluidity with definitions" and illustrates it well with the anecdote about Keith Devlin. This is a skill distinct from pure "analytical reasoning," as it requires comfort with definitions that are at once precise but also open to (frequent) change. The process of forming and changing definitions is creative and imprecise, and falls into what is sometimes called "conceptual reasoning." (A programming analog might be API design.)
- Several of the other points are tools for figuring out what is true, and for precising imprecise statements. For example the need to "teas[e] apart .. assumptions" is only natural when reading papers with Theorems that have very precise conditions .. which do not exactly hold in the case you need! In many other "analytical" contexts pre-conditions are not made as precise and arguments by analogy are considered acceptable provided the conclusion is believed. (A programming analog might be debugging when some implicit pre-conditions or invariants break.)