Cause they didn't have to write the NDK.

Because C++ is faster and can be compiled to machine code and, at least for now, you will need a 3rd party solution like Xamarin in order to compile and run C# on other platforms.

They'd be competing with Xamarin if they did that.

I think this is Xamarin, it's mentioned once on the page:

> ...or use these C++ libraries to build complete Xamarin Android Native or Java Native Interface applications.

It's a little unclear though

It is no Xamarin here! What they say is that you can use these C++ libraries from Xamarin or directly from Java (with JNI).