The resources at Synonym.com and Prezi explain the differences between narrative and descriptive writing (Synonym.com) or between narrative and descriptive essays (Prezi) but they are not very helpful at understanding the comment about Kuhn's The Structure of Scientific Revolutions. Especially Prezi bases the distinction between the two types of essays by focusing on the genre of the "personal narrative", which has nothing to do with Kuhn's book.
Definitions of "narrative" can differ considerably from each other, but narrativity is essentially the set of formal and thematic features that distinguish narrative texts from non-narrative texts. For example, some theorists point out that narratives present a sequence of events or actions that unfold over time. Other theorists state that narrativity is primarily determined by "experientiality" (M. Fludernik, 1996), by the "the quasi-mimetic evocation of real-life experience" (see "experientiality" in the living handbook of narratology). The iving handbook of narratology also points out that narrativity "has become a contested term". The preceding comments on the term "narrativity" are only marginally helpful in explaining the quote about Kuhn's famous book. The term "essay" is also hard to define because so many disparate types of texts have been termed "essays"; it is typically a type of writing that presents an argument rather than a narrative. (But, then, Wikipedia claims the term has also been applied to short stories.) Since I don't know the symposium speaker, I don't know why they said that Kuhn's book was not a narrative but an essay; I can only assume that they had in mind a clear distinction between the two types of writing.
The Structure of Scientific Revolutions is one of the most influential books in philosophy of science. I have not yet come across an introduction to philosophy of science that does not discuss it at some length (it often gets a chapter on its own). Kuhn introduced or revived a number of concepts to describe progress in science, such as "normal science", "paradigm shift" and "scientific revolution".
This is not the type of writing that one associates with "narrative" as defined by Synonym.com or on Prezi; the term "essay" seems more appropriate here. But the quote about Kuhn's book assumes that The Structure of Scientific Revolutions can be seen as a narrative, or at least as having aspects of narrativity. Why is that? Kuhn's book is also a book about the history of science; it replaces the way in which progress in science was usually presented (roughly as a steady accumulation of facts) with a new way of describing progress in science, i.e. by presenting as a type of activity that is dominated by a certain "paradigm" until that paradigm leads to contradictions and dead ends that force its rejection and replacement with a new paradigm. So in a way, Kuhn retells the history of science in a new way, which is why the term "narrative" applies here.