1-2 cocktails every other day, which is first given in the article, is 3½-7 a week. 2 per day is 14.

A carefully made cocktail (e.g. in the stricter European countries where the measures must be accurate) might contain 40-60 mL of spirit (2 US fl oz ≈ 60 mL), depending on the standard measure in use. Taking 50 mL, each drink is 20 mL of ethanol (40% × 0.05 L).

That's 75–140 mL/week, up to 280 mL/week if it's two cocktails a day.

The medical recommendation in the UK is not to drink more than 140 mL/week.

This is the low estimate. In the USA my experience is the barman pours in a bit extra (got to earn those tips!).

I'm not sure how we define alcoholism, but with the other mentioned drinks (beer, wine etc) at minimum the author was drinking at the UK recommended limit, in likelihood somewhat more than that.

I don't agree.

Drinking 1-2 cans of coke doesn't make you dependent on coke as an example. You can simply enjoy coke even though you don't need it.

If you feel upset/unhappy (even mildly) any day you can't have your 2 cokes, that's a dependency.

Perhaps, but that's my point with regard to the parents claim that 1-2 per day is definitely alcoholism. It may be for some people. Someone drinks 2 large vodka drinks, they are alcoholic. 1-2 glasses of wine, probably not.