The original author isn't trying to ban all screens from public life (e.g. screens that show bus information) or religiously avoiding them, it is obvious that by "screens" they specifically mean the "addictive entertainment that is usually delivered via screens". This does not mean they will run screaming from a screen at the doctor's that's displaying their vitals.
Actually, there's an analogy right there in your argument! We often say "he's been hitting the bottle" as a metaphor, that doesn't literally mean someone is hitting a bottle, it means that they are addicted to the alcohol in it.
It's the slime, not the glass.
https://www.youtube.com/watch?v=JPFIkty4Zvk
I am gross and perverted, I'm obsessed and deranged
I have existed for years but very little has changed
I'm the tool of the government and industry too
For I am destined to rule and regulate you
I may be vile and pernicious but you can't look away
I make you think I'm delicious with the stuff that I say
I'm the best you can get, have you guessed me, yet?
I'm the slime oozin' out from your TV set
[1] The drinking toast, not the television sitcom.