Is Denton “currently likely to be recognized as an exponent of fine-tuning arguments”?
In science, that would appear to be the Rare Earth hypothesis whose foremost proponents appear to be “Peter Ward, a geologist and paleontologist, and Donald E. Brownlee, an astronomer and astrobiologist” who wrote a book Rare Earth: Why Complex Life Is Uncommon in the Universe. The Wikipedia article on that hypothesis (surely a reasonably good indication of who is “widely recognized” on a subject) does not mention Denton at all – nor do the articles on Anthropic principle, Fine-tuned universe or Fine-tuning.
Even within ID-Creationist Apologetics, Guillermo Gonzalez and Jay W. Richards, through their book The Privileged Planet, would appear to be more widely recognized as exponents.
It would therefore seem more reasonable to term this a “Brownlee-type argument” (if we take a scientific focus) or a “Gonzalez-type argument” (if we take an ID focus) than as a “Denton-type argument”.