Precepts serve two purposes:
Purpose One is training the mind by changing your behavioral/emotional habits.
Purpose Two is improving one's karma by not creating turmoil in one's future that comes from the misdeeds.
In the long run One and Two help each other to get stronger. Together they gradually propel one further and further into Liberation.
Even if you take a liberal interpretation of the precepts you will train your mind and improve your karma.
In any case you should start from the most coarse offenses creating the biggest problems before proceeding to the subtle mental habits and misdeeds creating more subtle forms of trouble and suffering.
For example, being easily irritated and getting into fights all the time is a source of coarser and more obvious problems than killing mosquitoes or eating chicken and fish. So you should start with the first.
For example, craving sex to the point of rapping someone or seducing someone's spouse and breaking their family is a source of far coarser and more obvious problems than indulging in observing people of the opposite gender at a beach, so again it makes sense to start with the coarser one.
For example having a fragile ego and pathologically lying to cover up one's mistakes is a source of coarser and more obvious problems than not phrasing one's statements precisely enough to make sure they are absolutely true.
And as you correctly assumed, having a complex emotional trauma leading to a drug or an alcohol addiction is a source of much coarser and more obvious trouble than intoxicating one's mind with videogames, not to speak of indulging in an occasional beer.
From this it should be obvious that Buddhist path should be approached from coarse to gradually more subtle - by anyone and everyone, monk or lay.
If you think about it, the Eightfold Path gets into more subtle matters than mere Five Precepts, and the Four Jhanas get into more subtle matters than the Eightfold Path (i know they are included but you get the point). Within the four jhanas, the first jhana deals with coarse issues the second is more subtle etc. Entire Path is structured like that.
Obviously, someone who professionally pursues Anuttara-Samyak-Sambodhi is more likely to go all the way to perfection of practice, while someone engaging with Buddhism casually among other things will probably stop at preventing the most obvious troubles. How far to go is entirely up to an individual. The benefit is proportional to implementation, to whatever degree one eradicates potential causes of dukkha - to that degree one is liberated from it.
To summarize, it's not about liberal vs strict implementation of precepts, it's about coarse vs subtle causes of dukkha - similar concepts but not the same.