The Ziggs particle(s) Susskind is referring too actually has several names in the literature, and they aren't always consistent (they are sometimes labeled differently in different textbooks etc). What he is presenting is a simplified picture of a more complicated story, although he makes this distinction to emphasize that there is in fact such a story.
It is important to note that this is not the Higgs boson or the Z boson.
Basically what he is referring to are the physical excitations of the Higgs vacuum condensate. In the standard model, this is actually represented by a 4 component field of 'Higgses'.
I will call these guys H+, H-, H0, h. This field interacts (in a complicated way) with 4 different massless gauge bosons that I will call W1, W2, W3 and B, where certain linear combinations of the W's mix into states that then get eaten by the Goldstone bosons in order to finally create the massive W+, W-, Z (and residual massless photon).
The Higgs boson (the h) is basically the residual excitation of the radial excitation of this full potential.
Flip Tanedo does a good job of explaining this in a series of posts.
http://www.quantumdiaries.org/2011/1...etry-breaking/