A recent paper by Massimo Pigliucci http://philpapers.org/archive/PIGNAA.pdf describes what he sees as "scientism" in the output of the "New Atheists". There are some points raised which deal with real issues in some of the writings of the so-called "New Atheists" (such as how Sam Harris deals with moral values in his book "The Moral Landscape") and yet the premise of Pigliucci's paper seems deeply flawed - the validity of the term "scientism" is far from established, and the label "New Atheist" isn't coherent.
It has been said that "New Atheism" appeared as a phenomenon in response to the 9/11 attacks in 2001, a necessary reaction to the taboo against criticising religious faith, as faith could no longer be seen as a harmless personal matter. But is this really true? There seems to have been little if any coordination between the "Four Horsemen" of New Atheism - Dawkins, Harris, Dennett and Hitchens. Harris seems to have been motivated by 9/11 to start writing, but Hitchens' book critical about Mother Teresa "The Missionary Position" was first published in 1996. Dawkins atheist activism was first made public in a TED talk in 2002, as a reaction to religious attacks on science in the USA. Dennett's rather mild book "Breaking the Spell" (2006) was not an atheist rant but was an attempt to encourage the study of religion as a natural human phenomenon. So, there was no founding event of a "New Atheist" movement, simply a label applied to a group of writers, philosophers and scientists who happened to be visibly discussing religion. The label "New Atheist" is not a useful one, as it's far from clear what it's actually labelling.
As for scientism, Pigliucci breaks this down into two aspects - the first is the over-use of the label "science" for a range of human activities and the second is the rejection of the importance of philosophy. There is much to discuss here, such as the question of what is a useful definition of science, and the question of moral realism and its relation (if any) to empiricism, but that's not what concerns me about Pigliucci's paper. What concerns me is trying to associate these issues with atheism. There is a much broader clash between science and philosophy, and there is no necessary or even useful connection with atheism.
Rejection of philosophy by scientists is nothing recent. The Physicist Richard Feynman said "Philosophy of science is about as useful to scientists as ornithology is to birds". Another physicist, Stephen Hawking, has a well-known antipathy towards philosophy. There is on-going mutual distrust between much philosophy and science which for science takes the form of a rejection of the idea that philosophy has anything at all to contribute to our understanding of reality, and for philosophy takes the form of a tendency to drift away from naturalism and physicalism. This is a fascinating and important area of conflict between two great areas of human understanding, and it has nothing whatsoever to do with an atheist movement, and to try and look at it in that very limited context is to misunderstand the scope and depth of the conflict.
Let's try and drop the "New Atheist" label. It's misleading and unhelpful when trying to understand the history of belief (and lack of belief) and the fascinating interactions between philosophy and science.