New Atheism names a particular moment rather than the position as a whole, and reading it as the definition of atheism is a mistake. Between 2004 and 2007 four books (Sam Harris's The End of Faith, Richard Dawkins's The God Delusion, Daniel Dennett's Breaking the Spell and Christopher Hitchens's God Is Not Great), sold in numbers no work of unbelief had reached before, and their authors were widely called the four horsemen. The setting was the years after the attacks of 11 September 2001, and the case being pressed was not only that religion is false but that the deference customarily shown to it is dangerous and should stop.
What was new was reach and tone rather than argument. Most of the philosophical content had been available since the eighteenth and nineteenth centuries; the novelty was a mass paperback audience and a deliberate refusal to be polite.
The reaction from other atheists is usually left out of the story and is the more interesting half of it. The sociologist Stephen LeDrew argued in The Evolution of Atheism (2015) that the movement was itself an ideology, scientistic in its assumptions and incurious about what religion actually does for the people who hold it. Others objected that its treatment of Islam slid from criticism of doctrine into hostility toward Muslims, a charge pressed hardest against Harris and against Hitchens, who also supported the invasion of Iraq. Historians of science disputed its background assumption of a permanent war between science and religion, which specialists had largely abandoned.
The movement then fractured in the 2010s over questions that had nothing to do with God: disputes about sexism at conferences from 2011 onward, and the short-lived Atheism Plus project, which tried to bind atheism to a set of progressive commitments and was rejected by many atheists on the ground that atheism entails no commitments whatever. That argument is the clearest demonstration of the point made in the first article. By the late 2010s few people were claiming the label.