I think this is a problem with your URLS, the download link button is working but it is just redirecting to an index.php page instead of initiating the download. If you notice, the download hits are not being updated, if it was a problem with the file this would be updated. It looks as if the plugin is never being activated when the link is clicked, something is preventing the download URL from working.
You might look at enabling the .htaccess file, the Joomla URLS with mod_rewrite often seem to work better than the ones without.
You could also try changing the headers for the download file to specify a pdf, you would need to edit line 344 in the spiral_freedownload.php file, change:
header("Content-Type: application/octet-stream");
to
header("Content-Type: application/pdf");
I don't think that is the problem but it might be worth trying.
It could also be a problem if you have given the plugin field a default value other than 'spiral_freedownload' in the custom plugin field settings. This value must always be the system name of the plugin field for custom plugins, otherwise they may not work properly.