He just wants to look tough "Look at me, I'm in NYC and I'm not complainin'!"
It's like he wants respect for not complaining about a storm, because he thinks this makes him some kind of Ordinary Guy Hero. That's an entire sub-persona for him. "Hey, I'm an ordinary guy, I don't like Prince! Give me Bruce, amiright?" "Hey, I'm an ordinary guy, you know, I like Brett Favre." "Hey, I'm an ordinary guy, I like my hotel clerks to treat me with some respect and give me the pillow, ya know?" "Hey, ordinary guys, help me out: don't you hate it when some fancy-pants businesswoman on the plane talks too loud? Seriously."
He's appealing to audience to affirm that there's nothing at all wrong with Peter King. He's just telling it like it is, you know, for all of us Ordinary Guys out there.
What makes it sad and awful is that the vast majority of ordinary people look at a bad snowstorm in the news and go "Jeez, that SUCKS. What a pain in the ass." Because ordinary people empathize with our fellow rank and file. King can't because he's not a fucking Ordinary Guy. He's an entitled, wealthy, asshole. It's the definition of pretentious.