I'd be interested to know what 3 times more mean. If your chance of brain damage is 0.5% normally and jumps to 1.5% with moderate drinking, that isn't too bad. If it jumps to 10% to 30% that's another story.
If I'm reading Table 3 in the study correctly, when accounting for a bunch of possible variables (sex, age, exercise, etc), for every 10 units of alcohol consumed per week over 30 years you'd expect to see .19% decrease in hippocampal volume (0.08% to 0.30% decrease at 95% CI)