Is it possible to export a Grasshopper definition as a standalone script or application?

Short answer: no.

Long answer (edited/elaborated from posts by David Rutten, in this post):

There is no single script running behind the scenes of a Grasshopper definition. A definition consists of a runtime database of instantiated types which are defined in a collection of .NET assemblies. There is no restriction on what language was used to create those assemblies, though VB.NET and C# are the only ones I use.

If all you are looking for is a textual representation of a definition, try selecting your definition, copying it to the clipboard, and pasting it into a text editor. When you copy a set of components, an xml string is put in the clipboard which is identical to (well, very similar) a ghx file. It does not contain any of the logic of the components, merely which ones are hooked together.

However, if you are looking for something that reproduces the complete functionality of the definition, this is unfortunately impossible. There's just no way you can transfer all the logic running inside a Grasshopper file to a stand-alone executable. You'd have to provide mirror images of the Grasshopper SDK, the RhinoCommon SDK and the Rhino SDK. And then of course if you're dealing with 3rd party components you might get into even more referenced assemblies, some of which are copyrighted.

The only way to run the logic embedded in Grasshopper gh/ghx files is to run them through Grasshopper.