I have also never seen the word derivatives used in this context. Isn't "derivatives" usually used to describe options, futures, warrants, etc?

Derivatives in that sense are used to add some leverage on a bet and are known for their high risk, compared to the risk in directly owning their underlying equity securities. They aren't directly related to the underlying (same idea in calculus: y = f(x) ≠ dy/dx). I don't see how this adds additional risk in addition to the risk associated directly with owning Facebook stock.

While this technically is a derivative (underlying is Facebook stock), I think using the term "Facebook derivative" is a bit misleading.