That link is missing.

As I remember it, from David Gerrold's book, "The Trouble With Tribbles", it was a group improvisation on set. My copy of the book is probably somewhere around here almost 50 years later, but a minute's look didn't unearth it.

As I recall, Spock was supposed to knee someone in the head!, and, as you say, he balked at it.

Then another actor said, as if this were a well-known thing, "Hey, what about the Vulcan Death Grip?" The director asked, "What's the Vulcan Death Grip?" and Nimoy just walked over another actor and did the move you see in the picture, and the actor "passed out" and fell to the ground. Fun stuff!

The name got changed to "Vulcan nerve pinch" for obvious reasons.