Unfortunately, the track record of self-described atheists in places such as the Soviet Union and Communist China do not support the author's contention.
The sad truth is, human beings are all too willing to commit evil for whatever reason (or no reason at all). Religious belief can motivate violence and oppression—but so can such ideals as peace, freedom, brotherhood, equality, and prosperity. Even love can be a motivation for evil acts.
Atheists are subject to the same appetites, passions, and weaknesses as other human beings. Perhaps what the author really means is that humans must rid themselves of all emotion and become dispassionate logic machines. I would be interested in hearing how he would manage that feat.
This is an interesting error of argumentation that atheists often make.
Strictly speaking, nobody has ever killed anyone over "religion". Religion is a category, not an entity. People kill each other over particular religions, not over "religion" in the abstract.
Given that people kill over particular religions, referring to people killed by "religion" or on behalf of "religion" is an error of false generalization.
To put it concretely, if Muslims go on a rampage in India and murder Hindus, how does that somehow impugn Christianity? (Conversely, if we consider people killed by Christians over religious differences, how does that reflect badly on Hindus?)
And as you correctly point out, sin, including mass murder, is a part of the human condition. There is no religion whose members are exempt from that, and atheists certainly aren't.