A destination doesn't point to a range of pages, but to a specific page (or more accurately, to a specific view within a page), so you would need to figure out the range of pages based on the first page of the chapter you want to print, and the first page of the next chapter, minus one (unless it's the last chapter in the file, in which case it should be to the last page).
Also, you will have to know the names of the destinations in advance to be able to do that, as a script can't find out what destinations exist (or don't) in a file.
Assuming you know those names (and that each chapter begins at the top of a page) you can use something like this for that (let's say you want to print "Chapter1"):
var originalPage = this.pageNum;
this.gotoNamedDest("Chapter1");
var firstPage = this.pageNum;
this.gotoNamedDest("Chapter2");
var lastPage = this.pageNum;
if (lastPage>firstPage) lastPage--;
this.print({nStart: firstPage, nEnd: lastPage})
this.pageNum = originalPage;