Ah, Scrivener is a great tool for writing! Because it has all those features (cork boards, multiple drafts, separate chapters, etc), it uses a fairly complex file structure to store things in. There isn’t a single file that you can look at, to see how many words you’ve written overall or in a particular section. There also isn’t (or wasn’t when I last looked) an API you could use to retrieve such a thing from the system.
There have been several people who’ve produced workarounds to this, though: Autodata from Scrivener? (Ideas, please) - #2 by dreev is one, and definitely check out Tracking writing goals: Scrivener + Dropbox + Beeminder « The Markos Giannopoulos Blog.
You can see all the discussions with http://forum.beeminder.com/search?q=scrivener
As you mention, the only pure word-count goal type in Beeminder is the URLminder goal, which just retrieves whatever is at the end of the URL you give it, and counts the words over there. Basically, people’s workarounds involve doing some scripting to get text to a destination that URLminder can then see!