There are three ways I have thought about to solve your problem:
Using Abstract Syntax Tree Parser and Visitor
One way to solve your problem would be to use abstract syntax tree parser and visitor in order to automate the task of scanning through the code and documenting it.
The resources here will be of help:
-http://ramkulkarni.com/blog/understanding-ast-created-by-mozilla-rhino-parser/
-What is JavaScript AST, how to play with it?
You usually use a parser to retrieve a tree, and then use a visitor to visit all the nodes and do your work within there.
You will essentially have a tree representing the specific library and then you must write the code to store this in the def format you link to.
Getting a Documentation Generator and Modifying
Another idea is to download the source code for a documentation generator, e.g. https://github.com/yui/yuidoc/
By modifying the styling/output format you can generate "documentation" in the appropriate json format.
Converting Existing Documentation (HTML doc) into JSON
You can make a parser that takes a standard documentation format (I'm sure as Javadoc is one for java there should be one for javascript), and write a converter that exctracts the relevant information and stores in a JSON definition.