I think Logit's sample code is coupled very tightly to Excel. E.g. the Application.Something-Methods need to be adjusted for Access, Workbook/Worksheet reference will not work, etc.

I published an extensive info on ZIP-Archives with VBA and the Shell32 libraryon my website. It is based on the same approach of using the built-in Shell32 libaray, but it is split into smaller and more digestible procedures, which should work in any VBA enabled application.