Is it me, or does the opening quote not make coherent sense? He talks about writing, and then goes on about acting talents?

Narm is something which was intended by the show to be serious, but ends up being laughable/cheesy/pathetic. Narm Charm is when you end up feeling like the lame thing doesn't kill the drama after all. I really don't believe this fits:

"While Gordon Ramsay blowing his top may be sometimes hilarious, there are times where you actually felt sorry for the ones being scolded to, and you feel like he is bringing you down as well."

The reactions provoked are intentional, as it's a reality show, and not a rubber suit or badly written line. It's just a guy getting angry with no particular intended emotion; they know some people will laugh and some will bite their fingernails in suspense and they play to both sides. Thus, the entry has been removed, but preserved here in case the original poster or someone else can figure out a more fitting trope for it. (Sorry; I couldn't think of one myself.)

"The dance scene between Robot Zoe and the lab assistant who seems to have a crush on her should be cheesy as hell but it comes off as rather sweet."

I have absolutely no idea what show this is from, even after Googling "Robot Zoe". Could someone please explain?

How can we forget the trope originator, the great linguist Narm Charmsky?

Narm is when over acting breaks suspension of disbelief. I believe narm charm is when you're used to having damaged suspension of disbelief and either the show still causes the desired emotion at high level or it causes the desired emotion and the person knows that if they were suspending disbelief the show would be as good as a show should be. If one of my theories is correct than Narm Charm is dependent on the state of the viewer and is actually just a good show that didn't suspend disbelief well enough for 'some' viewers.