This idea of atheism only appears to deal with a certain kind of God about whom specific claims are made. The kind of God JWs have. I don't think this definition of atheism takes negative theology into account. That God can exist and not-exist, or neither, without being bound by definitions. When I think of God I think of God in these terms, or not in these terms, as the case may be.
http://religiondispatches.org/way-beyond-atheism-god-does-not-not-exist/
The atheisms of most committed, principled atheists are often not more than mirror images—inversions—of the theisms they negate. In On Interpretation, Aristotle wrote, “Affirmations and their corresponding negations are one in the same knowledge”; therefore, one can discern from many atheisms their corresponding affirmative theologies.
Turner also writes that, very often, the theisms attacked by atheists are not very interesting; therefore, the atheisms of most committed, principled atheists are not very interesting. Why this is so is not clear; perhaps it is because in many cases theism was abandoned before it was allowed time to develop into something of substance.