I've heard both. That drinking alone is the definition of alcoholism and also that it doesn't matter; if you're alone or in company, if you need a drink, can't stop once you've started, or you rearrange plans to accommodate booze over other things, you have a problem.
But, in reality, having watched my mum drink herself to death alone in her room vs watching people who are functional alcoholics going out for 6 pints after work, if I HAD to pick one (obviously, I'd rather lick neither), I would 100% pick the pints after work scenario. But then, for some people, that then morphs into the drinking alone in your room scenario...so who knows?
A friend of mine who is in her 70s says drinking alone is the definition of alcoholism, so wonder if it used to be?
Another friend of mine is a doctor and she sees a lot of women in gastro wards, seriously, seriously ill because of chronic alcohol consumption and many of them are naice, middle class ladies who just drank a bit too much. Not like my poor mum (a stereotypical alcoholic, poor thing).