Meaning of temporality in this line

My parsing: The artist's exchange is like chess because both exhibit: A competitive rivalry - two people compete to be heard/win (a tautology as competitor and rival mean the same thing) complex temporality: there is a complex situation that exists statically (ie is not exclusively of the moment) but also changes over time.

Part of the problem is that the word temporality has a wide range of meanings. In some cases it simply means relating to time, historically it has also had a specific meaning relating to the earthly possessions of the clergy. [https://www.merriam-webster.com/dictionary/temporality] Your wikiwand link [ https://www.wikiwand.com/en/Temporality] again highlights quite specific and divergent philosopical uses.

Without examining in more detail both the review, the artist's exchange and the critical reactions, it appears that the "complex temporality" refers to the interplay between the historical context of the art and the impact of the comments and discussion on that context. That weakens the analogy with chess but more closely describes the temporal complexity of art criticism.

I have a personal opinion which has no place in these pages, but my advice to academics for whom I edit, is to be as specific as possible. "Vagueness unsuccessfully masks a lack of clear thinking. Nail what it is that you really mean and everyone will understand your observation."

a complex temporality

A complex issue concerning the present condition rather than an eternal truth

OED

temporality

3. The quality or condition of being temporal or temporary; temporariness; relation to time.

1635 E. Rainbow Labour 11 Though in the act of our labours..we place temporality, yet ought we alwayes before our intentions to set æternity.

1659 H. L'Estrange Alliance Divine Offices v. 158 As the Western Church observed this very day [All Saints day], so did also the Eastern, or at least some other, in temporality and point of time very near it.

1678 T. Jones Of Heart & Soveraign 587 What can any mortal excellency, that has..perishing temporality stamp'd upon it signifie to Christians, who are not of this world?

1909 Westm. Gaz. 15 May 4/1 Gaining thereby the attributes of eternity, without losing its own qualities of temporality.

Temporality is (i)that which an issue, concern, matter, etc., that will pass in time, i.e. as opposed to a matter or concept that is eternal; (ii) that which is related only to current times, i.e. those things that are happening now (often with the nuance that these things are temporary.)

The "complexity temporality" here implies that the pieces on a chess board keep on moving. There might be moments when the black is ahead and moments when the white is ahead. My father suggested this answer and this is the only response that made sense to me.