The classic gait disturbance associated with
chronic alcohol abuse is ataxia, indeed. However, this is basically due to thiamine deficiency and constitutes the "Wernicke" component of the Wernicke-Korsakoff syndrome ("Korsakoff" is accompanied by amnesia, confabulation & hallucinations). The Wernicke component is also characterized by nystagmus & opthalmoplegia. So, any gait disturbance in the context of chronic alcohol abuse is a "korsakoid' variant, if I am allowed the term. (Also, don't forget flapping tremor, a sign of hepatic encephalopathy, that is associated with cirrhosis, which in turn is associated with chronic alcohol abuse. But in this case, the reason is impaired ammonia metabolism, it is not a sequella of alcohol).
Gait disturbance in
acute alcohol intoxication may also present in a similar manner, ranging within a spectrum (from impaired co-ordination to ataxia, to severe co-ordination disturbance, to coma and death) according to the amount of alcohol consumed.
In either case, one cannot definitely determine that the lesion lies within this or the other area of the CNS, because the cause is rather generalized (impairment of glucose metabolism in the case of chronic alcohol abuse; generalized & direct toxic effect of alcohol on the neurons, in the case of acute alcohol intoxication). It is possible that the cerebellum and the cerebellar projections to the motor system are more susceptible to damage than other areas of the CNS, perhaps due to variations of the blood brain barrier, but I am not familiar with any consistent data

.
Finally, I'd like to add that it is remarkable that alcohol has beneficial effects on patients with idiopathic tremor (NEUROLOGY 2005;65:96-101). This may suggest that alcohol shows some predisposition for the system of co-ordination, but I am not sure that this could be proven by, let's say, a pathologic exam of the cerebellum or its projections.
Any further input would be welcome!