You know what happened? He apologized off-the-cuff, and then got angry with himself for being bullied into an apology, so he recanted.
Regardless: if King had problems with Kosar's comments, he should address their substance, not call the guy drunk on the air. It's unfair, cheap, and unprofessional to call someone out as "drunk" unless you, you know, actually know they had been drinking. If someone of note (let's say, I dunno, Bill Belichick) called Peter King "drunk" on the basis of some of the stupid shit that he's written, Peter King would absolutely lose his mind.
It's "over the top" to call someone appearing publicly/professionally "drunk." You're basically calling them a loser and completely un-credible. Period.
However, to say that Kosar, who has a history of problems related to multiple concussions sustained during his career, sounded "drunk" isn't just over the top, it's fucking insensitive and completely hypocritical given King's pooh-poohing about player safety.
Applied to a random person, it's a churlish, unprofessional, bullying thing for King to say. Applied to a guy like Kosar, King's just being a flat-out asshole. That he is incapable of admitting that to himself is no surprise.