This will not capture a significant percentage of the former drinkers who are non drinkers. So contrary to your assertion, the current study did not truly separate out the two categories.
It did the best that any survey can do - this is medicine not precision science. It will not capture those who were moderate drinkers and who then stopped since they would have no medical problems (indeed the study shows they would have less chance of a medical problem). However this would bias the non-drinkers to look more like the moderate drinkers i.e. it would make non-drinkers look healthier.
As for former heavy drinkers I see no reason to suspect that these would end up as non-drinkers over moderate drinkers unless given medical advice that they needed to stop - in which case there would be a record and they would be classed as former drinkers. So the only way you can achieve what you claim is if there are a lot of heavy drinkers who did not develop any medical problems related to their drinking and whom all stopped drinking completely without any medical advice to that effect. This seems highly unlikely.