"However, atheism is not a belief system; it is not really an "ism." As the name implies, it is simply "not theism."
This is always a curious rebuttal. If Atheism is merely a lack of belief that this or that entity or type of entity exists, It is a purely subjective matter and of no rational or cognitive value in the game of giving reasons or discovering anything about the world as it is separate from our minds. Neither your nor my beliefs constrain the world in any way whatsoever.
However, as soon as the atheist steps into the light of a public form and says "I lack belief that this or that entity exists and you should too" your definition of atheism is immediately inadequate to describe the position they are presenting. What then do we call the person that is an atheist and thinks other people should be atheists too? They clearly are not just atheists as you have defined them. Their position is not just a personal lack of belief that a certain type of entity exists. Rather, their position is also that this lack of belief is the "right belief" to have, either for pragmatic, evidentiary or correspondence reasons. So, this atheists that steps into the public forum is either making an epistemological claim or an ontological claim, not just a claim about their lack of belief.
This is not as innocuous as some might think. If you have ever objected to someone that they justify their preferences about a policy of social importance (say abortion) by some sort of religious belief and therefore is not actually justified, you have, implicitly, stepped into the role of the atheist that steps into the public forum to announce that everyone should be atheist too.
As such, if your definition is the proper definition of atheism, the only time I should hear an atheist position is in response to some missionary or some other such thing. There should not be books titled "The God Delusion" or "Why Atheism is Right" or any of the like.
P.S. With respect to abortion, you might argue that the judiciary cannot uphold a law on the grounds of that religious belief. However, the legislation need have no such qualms. Their reasons can be as simple as the majority of people want it (even if those individuals that make up the majority have religious reasons for wanting it), and it does not conflict with clearly enumerated rights protected by the constitution (if they live in a country with such a thing). I concede, this last point, of course, might be very much in contention (depending on the country).