No, your suggested answers aren't quite the meaning here. In the above paragraph, it's obviously a question from some kind of health index, and one of the questions concerns how much alcohol they drank per day. If people drank a certain amount of alcohol each day, they got one point on the index (meaning this is a healthy thing ), but if they drank more or less than the specified amount, then that is considered not as healthy, so they did not get any points on the index.
As to your suggested examples using " no point":
1)He always focuses on no points. (meaning he can't seize the key point)
NO THIS IS NOT MEANINGFUL
2)I got no pointS. (meaning I got nothing) Yes, this is possible but only when you're talking about something that gives points for doing or not doing something, and if you got no points it means you got zero, not a 1 or 2 or however many point were possible. It doesn't have a general meaning of " got nothing", e.g., "I got no points from his lecture." (we wouldn't say that but we would say "I got nothing from his lecture.")
