Is the video for this talk available?

Does anyone have a lead on that awesome clip that makes contact with the pins and breaks them out to headers?

It's called a "test clamp" or a "test clip". Here's an example at SparkFun [0].

[0] https://www.sparkfun.com/products/13153

Let me recommend something else that is capable of doing this and more:

https://sensepeek.com/pcbite-kits

It's an IC test clip. I believe this is the one pictured: https://www.sparkfun.com/products/13153

What you mean is probably the "Pomona Clip".