It is because amp removes all javascript. So, you need replace [download_link] with <a href="[download_url]">[link_label]</a>, but only public downloads will work there.
Not sure which template is using by which package, you need to create a page template as per your need from Admin Menu Downloads Templates, and you can use this add-on http://www.wpdownloadmanager.com/download/wpdm-default-values/ to apply the template for all package in a single click.
test page: http://members.nrocnetwork.org/resources/download-package/test-gdrive/ , 2nd attachment is working fine, please remove and reattach first one, that also should work, however the url and download process almost totally handled by google drive, wpdm simply get the url and attach.
As both are remote file, you server will not be able to create zip file from those, so full package download will not work here.
The issue is not with wpdm update, it was happening due to a meta value coming from WPTouch Pro plugin, however I’ve added a patch to avoid it in your installation, also added in my side for next update.
