The 'Variables' button is nowhere to be seen.

This is either documentation issue or missing feature. The Variables button mentioned as (probably) the only source of information about build variable names is simply nowhere in the GUI.

It also does not appear on any screenshot on that help page. If it exists, it should be documented sufficiently enough so that users can find it.

And the list of variable names would also enrich the documentation, button or not. I hope the list will appear here: http://stackoverflow.com/q/34271859/607407