A common option used to export all Content is via the Data Export Service, although this will not be always an option. Solutions via AppExchange are available to help customer with these particular requirements where the Data Export Service is not possible.
One workaround that can be employed is to have all "Content Files" shared to the user performing the export in this case the System Administrator.
1. This can be done by the Content File owner in the UI by going to the File Detail Page and clicking on Sharing Settings and selecting the user where file needs to be shared with. More detailed information is available in Share Files with People in Salesforce Classic.
2. Above solution may not be always ideal specially when dealing with many files. An option is to use Data Loader to share the files to a particular user. Since you cannot use the Content Document Object to get the ID's, you will need to use another object to get the ContentDocumentID's.
Once the import is a success, the user where the Content Files were shared to will now be able to export all ContentDocuments with no problem via API and perform operations based on the "Sharetype" that was set.
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