Isn’t it obvious that online media would overtake print media? Wasn’t it a forgone conclusion from the moment that Tim Berners-Lee invented the Web that Newsweek (the print edition) would be supplanted?
It certainty seems so to me. From my point of view, of course Drudge Report took Newsweek’s readers and advertisers. And if Drudge hadn’t, another online media platform would have.
As AG noted, the market for newspapers was a brutal and competitive market. That market was an information processing machine, cycling through business models and exploring unknown reader demand curves to eek out whatever profit could be found.
But then the web was invented, and we see an explosion in the market reach of media producers combined with a lowering of costs in producing media right down to “pocket change”, as this very blog’s existence is proof of. The print media’s information processing machine was immediately out-classed by the online media’s information processing machine in every meaningful respect. More business models, more content, more readers, more advertisers great and small.
As far as I’m concerned, the only question is when print products achieve the same sort of museum quality that we now reserve for illuminated manuscripts or telegraph machines, not if. Online media has more experiments and more failures, more quickly launched and more quickly gone. The online information-processing juggernaut is both broader in scope and faster in execution than anything print can muster, as a basic property of its technological medium.
Sweet Talk 
I am so happy to have grown up in the age of personal computers and the web. I was never really a newspaper person. My magazine reading consisted of Nintendo Power.
From the first time my family got an Internet connection, I dived into the weird, the niche, the fan community. Print just can’t compete with that. Not when any schlub can start a WordPress site with some friends and fill it up with content on their off hours.
I’m only a little bit older than you, so my experience was mostly similar. The one thing I do miss about print though is that no one could edit or delete your archival copies. There was no link rot. I hope that one thing that advances in the future is an enhanced ability to save and archive what you find online to a personal server, rather than just retain a bookmark that may not work a year or five in the future.
That’s precisely the concern that led me to sign up for Pinboard and pay the annual rate to have the pages I bookmark stored in full on their servers, in the event that those pages disappear from the web.
+1