That's certainly not the normal behavior of "download as..." Try opening the .html file in a web browser (drag it onto the browser icon in the dock, or onto an open browser window to see what you get. If it's an error page of some kind, then the problem isn't related to your external drive, it has something to do with the link you're clicking on. I'm guessing that the link points to a separate page that then immediately initiates the download, rather than pointing directly to the download; this is common, but annoying, and is hard to easily work around.
An alternate option would be to just set your Downloads folder to the external drive, although that would then download EVERYTHING there.
Or... you could grab a secondary web browser (for example, if you're using Safari, get Firefox) and use it exclusively for downloading videos, so you can point its download folder at the external but leave your regular-use downloads folder on your internal drive.