I doubt he really meant addiction in the classical sense. I read it more as "Worst of all, becoming one of those assholes who can't put down their device and have a conversation like a normal human being". But I also limit my children's screen time, so I'm biased.
These "assholes" we see and are concerned about are, I think, mostly adults who did NOT grow up with such devices.
Our kids are taking our screens and gadgets for granted as much as we did TV (or whatever is appropriate for your age). It is a mistake to think that the effect of early exposure is going to be the same as it is for people for whom at some point it has been a fascinating novelty.
But careful not to conclude - TV was OK for me so these gadgets are OK for kids today. That's Pollyanna thinking. Every new gadget ups the ante on frantic messaging and addictive interaction. There's nobody looking for a sensible limit - they make the gadgets and we buy them, and one day off the cliff we will go like the lemmings.
Whether that is what he meant or not, there is a very strong case to be made that certain forms of content consumption enabled by computers (mostly the internet but software in general) are addictive in the classical sense (I assume you mean in the medical/DSM sense).
