That definition of anti-theism is very narrow. My preference is to refer to Dawkins as a "militant atheist," and reserve anti-theism for any position or thought that stands in opposition ("anti") to theism. That is how I have used the word in my essays.
For a comprehensive survey of "anti-theism" refer to this wikipedia entry, particularly the section titled, "Opposition to the idea of God." There, the Chambers Dictionary defines anti-theism as: "1. doctrine antagonistic to theism; 2. 'denial' of the existence of a God; 3. opposition to God."
Within the broader definition of anti-theism in the first definition, agnosticism and even some religious positions/postures are anti-theistic.
A particular case of the latter is the concession to the "myth of neutrality" on the part of Christian "evidentialist" apologists who debate atheists on the supposed "neutral" ground of "reason" in an attempt to "reason" to a probable God. However, to debate in that way is to presuppose that reason exists in a possibly godless reality -- that presupposition is anti-theistic. By adopting the epistemological standards of the unbeliever, the evidentialist violates Prov. 26:4, "Answer not a fool according to his folly, lest thou also be like unto him."
Here is the late Dr. Greg Bahnsen's discussion of the "myth of neutrality":
[Greg L. Bahnsen, Van Til's Apologetic Readings and Analysis, p. 146.]
"... the epistemological disagreements between believers and unbelievers [can] not be resolved in a neutral fashion, as though the issue of God's existence and character ... [can] be treated as secondary and thus temporarily set aside without any commitment one way or another while abstract philosophical issues [are] debated and settled. It is often, but vainly, imagined that once we come to agreement on our epistemology, we can apply those epistemological standards to the questions of whether God exists, whether miracles occur, whether the Bible is true, etc. By contrast, Van Til taught that abstract epistemological neutrality is an illusion and that, given the kind of God revealed in the bible, imagined neutrality is actually prejudicial against God.
"If God exists and is as the Christian world view claims, then His existence has an undeniable bearing on how we understand the process of knowing, the standards of truth and evidence, ultimate authority, and other crucial matters in epistemology.
"There is no pristine, religiously neutral, abstract 'reason' to which all men first swear their allegiance, only then to turn to such secondary matters as man's nature, moral character, relation to God, destiny, etc. The kind of man who is doing the reasoning already determines something about the way in which he thinks about reason and engages in reasoning. Thus Van Til stated, 'It is impossible to speak of the intellect per se, without taking into consideration whether it is the intellect of a regenerated person or of a non-regenerated person.'
"Van Til simply called for honesty and realism here. The metaphysical situation and object of knowledge (e.g., God's existence, the relation of created things to Him), as well as the psychological/moral situation and the subject of knowledge (i.e., man as a knower, someone using reasoning ability), cannot be ignored as we develop our views of knowing. 'Reason' is simply an intellectual tool, rather than an ultimate standard of knowledge (more authoritative even than God), and as such will be affected by the regenerate or unregenerate condition of the man using it. A person's epistemological behavior and commitments are ethical in character. According to Van Til, one's theory of knowledge is not neutral, but subject to moral assessment in terms of the ultimate authority to which one submits and which one attempts to honor."