(I worked at Google, with Closure, on some of these large JS apps. The Closure tech lead responsible for open-sourcing it is a friend of mine.)
It's true that all of Google's major customer-facing apps use Closure. However, I would not consider it to be a separate language, but rather a large component library and toolchain for developing JS apps at scale. The language is identical to Javascript, and Closure apps can be run uncompiled, they just take up more bytes on the wire and give the programmer weaker error-checking.
It is also very possible to write Closure without the type declarations - I've done it, frequently, for various doodles & easter eggs. They are non-optional according to the styleguide, but that's a style choice mandated for large teams. Typically, type annotations make working with large multi-developer JS apps much easier, but they're unnecessary for smaller one-off projects.
Also, any JS developer off the street can download Closure and use it to write JS apps, since it's open-source. If they want to use Closure Compiler they will probably have to forgo certain language features; I once tried to get JQuery to compile with it and it was basically a total loss. But the language should be completely familiar to anyone accustomed to working with Javascript. (You probably don't want to do this if you just have a small startup, since both the compiler and class library are designed for working with very large-scale apps and pay a large verbosity penalty for keeping things manageable, but it's possible.)