There is a fieldname for 'require_postcode' in the #__osrs_configuration table. But there doesn't appear to be any way to set this in the administrator's OS Property configuration.
Also, any field that is or optionally can be required, should set up the asterisk (*) in the frontend such that it is stylable via css. At present the asterisk is added, but it is not easily stylable. (e.g. it should be something like: <span class="required">*</span>.