First, Mr.
Dawkins is not the final, definite source for a definition of atheism. Second, you misconstrue his use of the term in that sentence, in which he uses it to elucidate a point he wishes to make--i strongly suspect that he was not attempting to redefine the term atheist, but only to make a point about monotheism in the context to the entire panoply of human theistic theorizing.
As for your definition of deist, when i consult Answers-dot-com, what i read does no violence to my understanding of the term:
Answers-dot-com wrote:One who believes in the existence of a God, but denies revealed religion; a freethinker.
Your comment about a deist being one who relies upon reason may be included in a definition which you have read, but not provided here. However, i am willing to assert to you here that such a contention is interpretive, and not axiomatically to be considered a part of the definition of a deist. Your case could probably be more easily made by asserting that those who espouse deism have notably claimed that they are motivated by an appeal to reason.
There was, in fact, a sect of Catholics who, abandoning the theological authority of the Papacy, claimed to establish their beliefs upon reason. Their thinking may not entirely appeal to you, as they held their belief in a context of remaining Christians.
Those were the Socinians. You might find it interesting to do a little online research on Socinian or Socinianism, as it is not a dead cult of centuries gone by--it has become a school of philosophical thought. It might appeal to you, or you might at least find their ideas compelling--i couldn't say. For my part, having learned of them, past and present, i am content to go no further with it.
