Assignment: Earth, which featured Gary Seven, is unique in several respects, and once considered together, may explain "why" but not "how" Seven resisted the nerve pinch.
First off, as you probably know, this episode was a "back door pilot" conceived of by Roddenberry in the hopes of launching a new series at a time when it looked like Star Trek was coming to an end. Had it been so, Assignment: Earth would have been the last episode produced. Because of its double duty as a pilot, this episode is considered by some to be the only Star Trek episode which wasn't really as Star Trek episode. As a result, the main characters of Star Trek are not the protagonists in this episode, Seven is. This in effect makes Kirk and Spock the antagonists of this story's "hero", a very unique position. Seven is the true main character of this episode/pilot, and as a result, Robert Lansing is the only guest star on Star Trek to be given a screen credit after the opening titles.
So, here comes my theory as to "why" the nerve pinch did not work on Seven. Roddenberry was making a point of setting Seven apart, and by giving him special immunity to Spock's pinch, placing him above the Star Trek characters in stature and importance. To Roddenberry Seven was hopefully going to be his future meal ticket, while at the time it seemed Kirk and Spock were soon to be a thing of the past.
Also worthy on noting, the last thing Spock said in this episode, and at the time it looked like it would be the last thing Spock ever said, was to Seven, "Live long and prosper, Mr. Seven". And Kirk says "and you too, Miss Lincoln". Those lines feels like a symbolic passing of the torch, or a sort of blessing being bestowed from the outgoing to the incoming. It is also interesting that this is the first time Spock says that famous line since it's inception in Amok Time, and it would have been the last time as well, had the show not been renewed.
As for how Seven resisted the Nerve Pinch, your guess is as good as mine, or any for that matter! I hope this was of some interest to you.