There are two different things you are discussing here - query and export. Query will allow you to select records where there is a certain contact type, and export will allow you to export only that contact type.

I might be misunderstanding though - I think your user might want to output only specific contacts in query? Query can still do this for you. If your criteria includes 'Contact type = Primary", and then you select Contact Name in your output, you will only see records that have a contact type of "Primary" and the Primary Contact's name.