After setting the permissions as per the vRanger 5.5 Installation Guide the backups were failing while using the non-admin account.
Error message: "Backup failed: An internal error occurred during execution, please contact Quest support if the error persists. Error Message: 3201 - can't open [DATASTORE NAME]..."
Solution: Currently I haven't identified the minimal permissions required, but I have determined that adding all privileges under "Virtual machine" > "Provisioning" enables the backups to perform successfully.