I notice that the phrase "as a critique" is used here, when "in a critique" or "for a critique" would have been more felicitous. "...qualities...essential...in a critique," or "...qualities...essential...for a critique".
The way it is phrased causes you to wonder if "critique" is supposed to describe the author: "...the author as critique," in which case it should have been "critic":
"...which of the following qualities was not
mentioned/deemed essential by the author as critic?" (i.e. in his capacity as a critic.)
It is not, strictly speaking, clear which was meant, and neither was clearly enough indicated that we could justify selecting one over the other. If your friend is a truly fascistic reading comprehensionist, he might be saying any choice is wrong since the question is, as written, syntactically "sprung".
Other than that, I can't see why it shouldn't be "C", like everyone else.