The full study is available online, and is linked to in the article. Their definition of "heavy drinking" seems to be more than three drinks per day, which seems like a reasonable definition to me.
The problem with that definition is that it still lumps modestly-heavy drinkers (two small beers after work, two glasses of wine with dinner) with really heavy drinkers (guzzle whisky until you pass out every afternoon).
If you plotted "health problems" vs "amount drunk" you'd probably see a fairly flattish curve from zero up to some level, combined with a sudden increase at very high levels of consumption. The "heavy drinking" number you're getting here is going to be a section of the flat curve combined with a section of the sudden increase, so the number you're getting doesn't tell you much.
