I have more than a sneaking suspicion that this project is essentially a proof-of-concept, and that it is not heavily used at Microsoft.
Further, how can you have a tool like this and nothing for generating type-aware documentation from your source code? Google uses jsdoc-toolkit, so this is a moot point for them. Either you guys are using this in an informal fashion, or documentation isn't that important at Microsoft, or you just haven't released the doc generation tool(s), which would be a really odd choice!
And TypeScript is just the language, so there's no API to document besides what your browser exposes in JS.
Even CoffeeScript had a manual very early on, and so did Dart.
I'm not saying "bad on Microsoft for releasing this!"; it's good they're starting to sort of figure out how open source works. Rather, like I said,
I think you'd be a damned fool to invest in this technology for any serious project.
Right now this is a toy.
I have my complaints about the library (certain dusty corners of goog.ui and goog.editor have hard-coded CSS classNames and Google URLs, meaning you have to use a patch queue to customize them) but I'm very pleased with the API documentation and examples. Google admittedly leans on Bolin's book (O'Reilly, 2010) too much for the community's manual-style documentation, but this is less crucial for a library than the API docs, and that book is really good :^)
The library has an extensive demo collection which is pretty nice too, and the demos generally include a minimum of 2-3 examples to show different ways to use library components (decorating vs. rendering usage of goog.ui package, for instance).
Google's real failure with Closure Tools has been marketing, but that is not my concern very much as a user. However, I see how this affects the library's adoption, so I've created a page at https://oinksoft.com/closure-tools/irc/ (I op the IRC channel) where I hope to aggregate more resources over time so that new users are able to get up-and-running without using Bolin's book.