If the way nature behaves and human history are reliable, murdering people for no reason is a perfectly legitimate course of action against those who are considered threats.
1) If they are threats, then there IS a reason to murder them.
2) Going by human history, any culture that acts in a psychopathic manner and starts to randomly kill people and make war on other cultures for no real reason tends to make a sufficiently large number of enemies, both within and without, that, sooner or later, they are killed in turn.
So in a Godless universe, why is psychopathy bad, if it is a naturally occurring behavior in animals?
Actually, given that the definition of psychopathy is actually inherently tied in with human sociological norms, it can actually be argued that, by definition, there is no such thing as a psychopathic animal. It is debatable, however, as it could also be argued that a psychopathic animal is one that doesn't conform to it's own sociological norms in a similar way as human psychopaths. This wouldn't be 'naturally occurring behaviour', though, except in the loosest possible sense.
Animals commit genocide. Animals commit rapes and murders, but if human beings are just another animal, where do you base your objective value judgment on God's or anyone's psychopathy, if values and even the notion of psychopathy are social constructs that are the byproduct of the human brain's evolution?
1) Animals tend to only 'commit genocide' or 'murder' for a pretty good reason - for example, in order to get food, or to remove a threat to themselves. As for rape, some animals rape, yes, others do not. Humans happen to be one that has evolved several complex societies where rape is acceptable in some, but not in others.
2) Yes, values and even the notion of psychopathy are a result of the evolution of human society and civilization and the understanding of them. This fails to make them meaningless or unimportant. Even if we were to decide God was not a psychopath, just a non-human entity with very different values, that still doesn't explain why humans should disregard our own values to obey his orders to kill other humans. Any other hypothetical non-human entity giving such orders would be seen as a clear threat to humanity.
On the Christian, God-fearing side, St. Thomas Aquinas justifies the removal of atheists, heretics, and sodomites because not only do they threaten the material well-being of society, for example, by accumulating wealth that doesn't circulate outside their sodomy trains, but also the spiritual health of the people.
The idea that these groups only circulate money amongst themselves is utterly ludicrous, and if the 'spiritual health' of people is not threatened by killing them, then 'spiritual health' is pretty meaningless.