Susan,
No, it isn't either. To be a parody it would have to introduce a fresh element that was not part of the usual plot. The fact that it has fresh text is most probably down to Kinloch's interference with whatever the Roxburghshire lady sang him.

The fact that some of these versions concocted around 1800 closely resemble burlesque doesn't mean they are. To be burlesque there has to have been some deliberate attempt at ridicule or comedy.