If you find yourself wanting to transfer a number of links, which you have entered as “Links” via the admin interface of your WordPress installation, from one WordPress site to another, this support article is helpful …

Import & Export Links — Support — WordPress.com

EXCEPT that my browser tried to save the file as a web archive. Choose “Source only,” and change the extension to xml.

Then upload the file using the Blogroll importer.

Works! with one flaw …

Unfortunately, it will not keep the link categories intact. You will need to update the category for each link. To save time, create a category in the new WordPress installation for the category most used in the old installation. Then select to have them all imported to this category. That way the majority will already be set correctly, and only the others changed.