First thing: the only people who care about journalists is other journalists. This is how it has been for a long time. Drudge is a journalist, so he pays heed to the journalist world, their triumphs and their downfalls.
The other part is that Drudge has a huge inferiority complex.
Drudge only has a high school education. He wanted to be in the media world, but always knew he could never penetrate it. He worked in gift stores in Los Angeles, while totally understanding the media world that operated around him. He was of their caliber or better, but he simply lacked credentials.
Then the internet revolution happened.
Drudge found he could reach millions of people just like mainstream media. His edge was that he ran stories that the biased established media would not noit run. Paragon and career-maker for Drudge was....the Monica Lewinski story.
Newsweek knew of this story for weeks, and there was a story ready to headline one of Newsweak's issues. But Newsweak is famously pro-Clinton, so they decided to axe the story. So did Time Magazine.
Drudge went ahead and broke the story wide open, a story that revealed the mendacity of Clinton to the world, and the media fought tooth and nail to kill it and Drudge's scoop. That basically made Drudge's bones and assurred his place in 21st century journalism.