It's okay if you are writing a story about your personal reactions.
It's irrelevant if you are writing a serious critique, which should be about the content, not about your emotional response to it (assuming it is a critique of an informative work -- obviously, if you are critiquing something as a work of art intended to inspire emotional responses, writing about your response as some relevance.)
It's possible to blend the first kind of story with the second kind of critique, but you have to recognize the different roles of each, do it deliberately, and be exceptionally skilled (the set of people who can do this and produce something worth reading is a proper subset of the intersection of the sets of those who can write entertaining personal stories and those who can write valuable straight critiques.)
That being said, tptacek's review seems pretty focussed on substantive critique with very minimal emotional distractions, so while I disagree with the categorical defense of the individual statements at issue as being appropriate to a straight critique of an informative work, I also think that the charge that the tone was inappropriate and a barrier to reading is overblown considering the fairly minimal level at which distracting emotional descriptions are present in the review.
