Why do the brains of cocaine-users shrink faster than the brains of non-cocaine users?
The mechanism of action of cocaine is dependent on pre-existing dopamine production and secretion. Normally, secreted dopamine is cleared from the synapse via the dopamine transporter (DAT) located on presynaptic dopaminergic terminals. Cocaine inhibits
this reuptake of dopamine, increasing it's duration of action on post-synaptic dopamine receptors. Thus, cocaine's effect depends on neuronal dopamine production. Without intrinsic dopamine, cocaine would have no effect. This is actual not exactly true though because cocaine also inhibits serotonin and norepinepherine reuptake transporters as well but the same argument applies to those neurotransmitters as well. 

The overall effect of cocaine on the nervous system is extremely complex as it prolongs the action of dopamine, serotonin and norepinephrine wherever those reuptake transporters are present. There is a particularly high density of DAT in the basal ganglia and nucleus accumbens. What these areas of the brain normally do is under intense study and debate. The accumbens may play a role in goal directed behavior and incentive salience, which is the attribution of value to various actions or objects in the environment. This is what naturally guides us to perform one action over another. The simplistic view is that cocaine "highjacks" this system such that cocaine itself acquires greater incentive salience than natural reinforcers such as food, sex, money etc. 

Getting back to the original question regarding why cocaine causes brain atrophy. This appears to be a finding quoted from a paper by the original inquirer. It is not obvious to me what the mechanism of this atrophy would be. I suggest you look at the discussion section of the paper from which that abstract was quoted to see what the authors suggest. However, to my knowledge, such atrophy has not been widely discussed in the cocaine literature but I could be wrong. 

For further information see Sulzer. 2011. How Addictive Drugs Disrupt Presynaptic Dopamine Neurotransmission.