We talk about "running text" to mean the flow of text in the main body of a document, in contrast to individual words in a list, or short structures like headings or footnotes. In the context, it seems that the editor is describing 2 billion words in extracts from running text, and not a list of 2 billion distinct words. It is reminding us of the distiction between a corpus and a dictionary.
However this does not seem to be an idiomatic or common use of the word "running". The information is a repeat from the introduction and probably should be removed or edited.