Question details:
Answer by Mike Mendis:
The term “atheism” and its definition are both muddied by the imprecise nature of the word “God.” Thus, the dictionary definition you cite is misleading at best. Before we attempt a definition of “atheism” or say what an atheist is, we need to define what we mean by “God” or at least say how we are using the word. Are we using it to refer to the Creator God of Christianity and Judaism? Or the Unmoved Mover of Aristotle? Or the many gods in the Greek, Roman, Hindu, Aztec, Mayan, and other pantheons? Or the Deist God of Thomas Jefferson, Benjamin Franklin, and other American Founding Fathers? Or the impersonal “God” of Einstein (and Spinoza)?
Einstein was, for all practical purposes, an atheist with respect to the existence of a personal Creator God, and yet he appears to have believed in a God of some sort, and used the word “God” quite freely, as in his famous quip, “God does not play dice with the universe.” In fact, he did specifically state that be believed in the “God” of Spinoza.
Thomas Jefferson was an atheist with respect to the Tritinitarian God of Christianity, a God who revealed himself to humanity, and he was openly accused of being an infidel and atheist during his lifetime. In a letter to his nephew, he wrote: “Fix Reason firmly in her seat, and call to her tribunal every fact, every opinion. Question with boldness even the existence of a God; because, if there be one, he must more approve the homage of reason than of blindfolded fear. … Do not be frightened from this inquiry by any fear of its consequences. If it end in a belief that there is no God, you will find incitements to virtue in the comfort and pleasantness you feel in its exercise and in the love of others which it will procure for you.” (See Letter to Peter Carr.) Yet he believed in a “God” of some sort, as is evident from his use of the phrase “Nature’s God” in the Declaration of Independence. (See Declaration of Independence – Text Transcript.)
Another problem with the dictionary definition you cited is that is assumes theism (or belief in the existence of a God) as the default position. Atheism cannot, strictly speaking, be a belief, since one cannot “believe” in the non-existence of something. Atheism is the rejection of various claims made by theists (as others have already pointed out). By this definition, one can be an atheist with respect to some or all of the claims made by various theists and still be open to the existence of something that one might choose to call “God” (as Einstein did).
With regard to belief in the supernatural apart from God, we would once again have to define what we mean by “supernatural.” Clearly, phenomena that were once considered “supernatural” (thunderstorms, eclipses, and so on) have been brought within the realm of the natural with the passage of time and advances in knowledge of the natural world. By “supernatural” do we mean “that for which we do not yet have a natural explanation” or do we mean “that which is permanently beyond the reach of natural explanation”? Scientists generally hold to the view that there is nothing “supernatural” in the second sense of the word. That is, everything that occurs in the universe has a natural explanation, even if we have not arrived at the explanation just yet. By the first definition of “supernatural,” it is possible for someone (such as an “atheist”) to deny the existence of a supernatural God (a being who is, by definition, permanently beyond natural explanation) and yet accept the possibility of other seemingly “supernatural” phenomena. This does not amount to a “belief” in the non-divine supernatural. It merely admits that some observed phenomena do not yet have a natural explanation and that such phenomena are commonly considered “supernatural.”
Finally, it should be mentioned that just like theists, atheists come in all shapes and sizes (and this is quite evident on Quora, where some people style themselves as “atheist” and yet seem to be continually arguing for the other side). There are hardcore atheists and softcore atheists and a whole spectrum in between. No dictionary definition (or even an extended definition) can do justice to the term.
Michael's-Eye View 
Very considered post. I particularly liked the message that atheism is not a belief. It annoys me when people think it’s like a religion.