He's rather overstating the confusion -- I know for a fact several of the authors he cites in the introduction go far beyond the short quotes he provides to detail what they mean, being well aware of the cultural ranges of meaning, within and between various cultures, of "god" and related terms. No professional scholar I've ever read thinks monotheism only refers to the number of beings which might be called "god" (although theoretically that could be a meaning, too).
Considering that he doesn't even try to put a noun next to "three" in his description of Christian Trinitarianism, I could make what I expect is a pretty accurate guess as to why he's promoting more confusion in the ranks than actually exists. (A guess weighed farther by who posted a link to the paper.
The word “God” is nowadays often used as a title, almost a proper name - in any case, a singular referring term. As such, it arguably does not admit of conceptual analysis.
Either he's highly ignorant of why God, with a capital G, is treated that way in English, compared to "god" with a lowercase g, within the purview of the philosophical and religious development of Western Civilization (in which case he shouldn't be writing academic papers on the topic), or he's intentionally salting the Pepsi in order to introduce straw man problems. Of course
"God" as a proper name/title in that cultural context admits of conceptual analysis. If it doesn't, then neither does the English word "god" without capitalization; I could assert (not even an argument really) very similarly, that its usage scope is so broad that it arguably (but with no actual argument) does not admit of conceptual analysis and then move along. That would be equally nonsensical, not only in relation to the actual history and status quo of the term, but in principle: these words don't exist in a conceptual vacuum, which is exactly why someone could even try to pretend they're too narrow (or broad) to admit of a conceptual analysis. If they couldn't admit of conceptual analysis, neither could someone analyze them conceptually enough to give a reader of the language any idea of what's being denied (or rather refused) for conceptual analysis!
Even Sdfhj, a gibberish I just made up now by plopping my fingers on keys, admits of enough conceptual analysis for someone to understand what it means for that group of letters to be a gibberish I just made up now by plopping my fingers on keys, and so also why not much more conceptually can be expected from it -- except also as a comparative example of the concept I'm critiquing here. Those letters aren't only a random accident generated with no purpose; and even if they were, my judgment about that status would still count as conceptually analyzing them to determine accurate facts and truth claims about that set.
So we have an author who intends to read between the lines about the conceptual meanings behind words, and his first evidence is an inability or willful refusal to talk about conceptual meanings of words that have a strong history of conceptual meaning, and to pretend that other authors are irresponsibly throwing the same words around without taking the time to explain what they mean by them -- when anyone who knows the authors will know this demonstrably isn't true. After this, to continue paraphrasing C. S. Lewis, why need anyone attend ever again to anything this person says?
He has started out with a shell game; I have better things, and also far more entertaining games, to be spending my time on, than seeing whether my inductive expectation from past experience is that he will continue with his shell game (even though induction isn't a perfect predictor of future trends).