By design, Vendors can only view and download the data of SDL TMS jobs that were assigned only to that Vendor. If the job was Multi-Vendor - different languages being assigned to different Vendors, then the download option will only be available to Administrators.
Archived Jobs in SDL TMS contain ALL data for the job, meaning if a Vendor could access the data, they could also access sensitive data related to other Vendors. Hence this is a designed restriction.