I think that, in large part, the reason people sometimes use the phrases “fundamentalist atheist” or “militant atheist” to describe contemporary atheists has to do with the high expression of confidence expressed by some atheists. Like fundamentalists who express a high degree of confidence on matters for which high confidence is (to put it politely) not warranted, so there are contemporary atheists who come across as more confident in their own beliefs than the evidence warrants. In the face of the enormous mysteries, enigmas, and perplexities of existence, expressions of confidence come across as being akin to religious certitude—and hence fundamentalist. Perhaps fundamentalist is the wrong word—but it is not entirely the wrong word. The analogy may be imperfect, but it is not wholly absent of meaning or relevance to the contemporary atheist phenomenon.
Perhaps “triumphalist” is a better word for describing some contemporary atheists. People who are triumphalist display outsized confidence in the essential correctness of their way of seeing the world and display little irony or self-doubt about it. You never get the impression from a triumphalist that he or she might spend any time seriously wondering if maybe he or she is wrong. And a triumphalist would not be caught dead “wasting time” reading the books of the other side—except perhaps to gather fodder for ridicule or apologetics. And triumphalists—whether of the religious or secular varieties—are really good at cognitive dissonance. Their triumphalism is at once sunny and utterly disproportionate to the reality of their actual situation.
So perhaps “Don Quixote atheist” is another way to refer to the triumphalist atheist. It is not unusual to encounter atheists who are living in a fantasy world that is impervious to anything outside of it. And circular reasoning keeps everything out that the Don Quixote atheist wants to keep out. To the Don Quixote atheist, everything in Atheist Land is rosy. Its leaders are outsized in their moral rectitude and intellectual vision, and the sun shines clear. There are no problems worth bothering about, and no difficulties (only apparent ones). To the triumphalist or Don Quixote atheist, the pessimistic atheist—or the atheist or agnostic who is a sympathetic listener and dialoguer with theists—or the atheist who is dubious of the leaders of the new atheist movement—has not absorbed how wonderful pure atheism is. It really is like being in an Ayn Rand-style cult for some contemporary atheists. There are outsized charismatic leaders, an obsession with purity, and an image (largely delusionary) of one’s ideology and movement being free of taint when practiced confidently, fully, and without apology.