Haoyang (+ Martin): Typings update

[fongandrew]

Per DefinitelyTyped/tsd#269, TSD has officially been deprecated in favor of https://github.com/typings/typings.

This PR switches everything from TSD over to Typings. You'll need to run make clean and make setup again.

The biggest differences between TSD and Typings are:

• Some Javascript libraries installed via NPM may function differently depending on whether they're used in a browser context or a Node.js server context. Typings supports different definitions for each environment, so references to definitions should be to the versions inside the typings/browser folder, rather than the typings/main folder. For the sake of simplifying things, I've changed most of the type references to typings/browser.d.ts (which contains all of the references) rather than enumerate them individually.
• TSD installs all definition dependencies in ambient (global) context, whereas Typings permits definitions to require other definitions in a non-ambient form. That can be useful if, for instance, a library uses the new ES6 import / export syntax for Javascript modules or if we want to bundle two different versions of a library with different type definitions. At the moment though, the only impact on us is that our definitions are stored in the typings/browser/ambient directory.