How to share files uploaded in "Files" related list to Community Users

Files uploaded via this related list will only be visible to internal users, and this field is not editable.

One thing you can do is post the file to the record via the Chatter publisher, and specify the visibility in your post. This would give the attached file the same visibility as the post.

Another option is to write a trigger and edit the Visibility field of the ContentDocumentLink that is created when the file is uploaded. Although you might want this to be context aware so that you don't do this whenever any file is created (and also requires some technical knowledge).

As citizen conn pointed out you can use a trigger to edit the Visibility to enable community users to view the file. Here's is the exact trigger you'll want so when internal users upload documents, community users can see it:

UpdateContentDocumentLinkVisibilityOnInsert on ContentDocumentLink(before insert)
     { 
       for(ContentDocumentLink l : Trigger.new)
       l.Visibility = 'AllUsers';
     }

Context: With Files enabled, Community users can only see files that were uploaded INTO that community. (i.e., when an internal user with a full SFDC license uploads/creates a file and adds it to a record, the community users can't see it, eventhough you've shared the file with "The Entire Company" AND the community users have access to view the record.)