...in a NetBeans RCP application, what additional JARs will you need to include for the Groovy Editor to work?

Leaving aside the debate on the current state & quality of the NetBeans Groovy Editor, so, assuming you need the Groovy support that the NetBeans Groovy Editor provides, you would check the Groovy Editor checkbox in the Project Properties dialog of your application:

As you can see, however, the Groovy Editor depends on other modules, some of which, in turn, depend on yet other modules, and so on. So, I clicked the "Resolve" button above and then created a ZIP distribution, to see which additional JARs had been included.

Until that point, I had only been using the "platform" cluster, which means that absolutely everything found in the ZIP's "ide" cluster and "java" cluster have only been included so that the Groovy Editor could be included, i.e., all thanks to clicking the "Resolve" button above.

Let's first look at what that means for the "java" cluster:

That's not so bad and kind of a side effect of Groovy being Java, i.e., a lot of Java functionality is needed.

Now let's look at the "ide" cluster:

So, in answer to the original question, if all you want in your NetBeans Platform application, in terms of editor functionality, is the Groovy Editor, then you have a pretty high price to pay. At the very least, I would have assumed that the project support JARs and the debugger support JARs would not be so tightly coupled with the Groovy Editor. That would be a cool thing to separate out from the editor support.