This example is unchanged from the default file that's there to begin with. The authpriv file has restricted access. To make this happen every startup, edit the rc call to syslog. Now the server is listening for log data from all clients who have been told to send their logs to the server. This tells the client to send its logs to the collecting server, as well as log them locally.
Redundancy is good.
Remember to restart the server and clients after making these changes. To make logging happen on startup, each machine needs an rc call to syslog. This should be default. You may want to change the mark setting, however. This will tell you if it's on the system.