Well, I'm no sociologist, but I think I'll take a few guesses as to why Richard Dawkins and New Atheism. This is just coming from my friends at school along with propaganda I've analyzed on Facebook and other Social Media websites. I seem to notice an overarching theme that is not scholarly, but pretending to be scholarly. Somewhat like randomly quoting Nietzche or talking about the philosophical lessons of the Bioshock series, especially when it's the most high-brow thing you've seen. This is just speculation from things I've examined, so I'm not sure about overall accuracy.
Faux Intellectualism: This is something I've seen in almost any sort of atheist anything outside of the Khmer Rouge and Communist China. It will constantly be hammered down that Christianity is false. Very little, if any reasons God (properly understood) does not exist will be provided. This is common among New Atheist literature. Richard Dawkins seems to be the only one who tackles arguments for the existence of God. Their approach to the Bible is even worse. Rather than try to show the documents unreliable, they just go ahead and call the Bible an "overrated fantasy book" or compare it to Harry Potter. This is just inane and the use of the fallacy Appeal to Ridicule. The spreading of this fallacy and rejecting false images of Christianity makes people feel smarter, which has a vast level of appeal for young folks who want to make themselves feel like an individual. I can relate to this because the feeling of being an individual was what drove me to become a Progressive Creationist, but I changed when I honestly thought of the theological implications.
Sexual Freedom: This is something that makes atheism very appealing to many people. I don't have to explain much here. This can be related to many other things and generally being held accountable for their own actions.
Rebellion: Sometimes, rejection of Christianity can simply be a rebellion against their parents or against their society. Some atheists/agnostics I know call themselves "rebels" often. This is a rather silly way of thinking. Just because something is popular doesn't make it false, just as something being popular doesn't make it true. Ironically, the appeal to atheism and liberal ideas seems to be in "rebellion", but I often feel like a rebel in my school and area for being a Christian and having conservative views. It's gotten to the point where I cannot bring up homosexuality or abortion in my school for fear of stirring up controversy. To be fair, though, other students have this limit, including liberals.
Moral Outrage: This is a very common theme apparent throughout the New Atheist diatribes and the literature of their followers. Ironically, there is no grounding for Objective Morality in a naturalistic worldview, so their moral outrage is only opinion. So why should I trust their claims over, say, Ted Bundy's? Many of their claims are also vastly inaccurate, but even if they were true, they would be committing the logical fallacy Appeal to Results of a Belief, which is when says that a claim must be true/false because of the results. This would be like arguing that Nuclear Physics must be false because it led to the development of Nuclear Weapons.
Ignorance to Science and Theology: When dealing with common misconceptions dealing with the Bible and Christianity, this quote from the Screwtape Letters comes to my mind:
"Jargon, not argument, is your best ally in keeping him away from the Church. Don't waste time trying to make him think that materialism is true! Make him think that it is strong or stark or courageous - that it is the philosophy of the future. That's the sort of thing he cares about."
Okay, that could have been used earlier, but I didn't feel like digging through the profound quotes to look for the specific one. It was similar anyway. Keeping people away from basic knowledge relating to the Bible and theology is a very common thing I see being done in atheist sites. Some have even thought that the verse "I am the Alpha and Omega, the beginning and the end" to be a contradiction rather than referring to God's nature. To them, God is just an invisible man in the sky who wears a beard and smites people. This is a strawman argument, and if anybody uses it, I feel like I'm talking Geology with somebody from the Flat Earth Society. Trying to keep people from Biblical knowledge by making the Bible seem silly is a similar tactic used by cults. I could probably relate many Cult-like tactics to New Atheists, but that's another thread.
Rather than come as the beacon of truth and sharing of research, for many the Internet come like the biting fly of ignorance. Here, misinformation can spread and fool millions. Propaganda can simply be passed as a "joke". Bigotry and ignoring scientific advancement can be seen as "progressive." The bite may not hurt much, but it carries nasty diseases. However, this can be stopped. For every biting insect there are predatory insects, spiders, frogs, and bats that hunt them down.
TL;DR version:
-Richard Dawkins gains appeal among those who are not very familiar with theology or philosophy.
-Appeals to emotion and ridicule make people feel superior to others.
-Makes people feel like they're something different.