Okay! So, as I understand it, Dawkins talks about how organisms are bent on (sorry, not being a scientist I'm not sure of the terminology) having the maximum chance of having its genes passed on - humanity is a 'survival machine'. Okay - so far so good?
But...what this means is that survival is inevitably the expense of other - different plants compete for the soil's nutrients, weaker creatures die while stronger ones live. This being programmed to (?) survival is inevitably violent, in that it means the suffering of others - not that the stronger creatures are nasty as such, they are just bent on / programmed to survive and therefore it's out of their control. Altruism happens, yes, but within a larger framework of competition for survival., and thus unconcious violence.
So, in Christianity, this urge / whatever for survival is met head-on in Christ. Christianity is basically a martyr religion. Jesus is the ultimate martyr who meets the violence of the Roman Empire with volunary self-sacrifice. The words 'I am a Christian' were a death sentence in the pre-Constantinian era. Yes, it's softened over the ages, and yes, Christians aren't very good at living up to this not fluffy at all religion. 
Sin is defined as living for oneself, and this self-centred living may appear altristic, but is based on a competition for survival, a competition we can't escape from, which is why some people end up more victim than sinner.
So when Jesus dies voluntarily, he not only challenges this, but as (as we Christians believe) God in human substance, he changes the nature of things so that all creation may start to be restored and freed from the competition struggle to survive. The lion will lie down with the lamb...
So what we see now (in this scheme) is a world still fighting for survival - which is why the Christian doctrine of eschatology (belief in ultimate restoration) is so important. In the meantime, Christians are called to 'take up their cross daily' and be what the NT calls a 'firstfruits' of the world to come. I could say much more about this!
There - that was quite long! And took blimmin' ages, as my computer is running very slowly!