Hello, I was having the same problem, where only the shortcodes showed up. I reverted to WordPress 4.8 and the previous version of Download Manager pro, and it works now.
To duplicate the problem, on my staging server. The download links were displaying normally, then I:
1) Updated WordPress 4.8 to 4.8.1.
— Download links still worked.
2) Upgraded Download Manager Pro from 4.6.7 to 4.6.8
— Download links broke, only shortcodes showing up.
The plugin behaves as if it is deactivated because all the menu items in the left side are gone, but the plugin is active.