Is it? I think we have a pretty good grasp of what "reasoning" means in mathematics and computer science, in particular with logic. Although to be fair we normally use the word "inference" in maths and CS to avoid confusion with what humans do informally, vs. what we do formally, with computers or without.

But it's clear that the author of the paper above is using "reasoning" to mean formal reasoning, as in drawing inferences from axioms and theorems using a set of inference rules. I think that makes the article's point very clear and we don't need to be splitting hairs about the different possible definitions or understandings, or misunderstandings of "reasoning".