As per my understanding the export functionality over here does the job of creating the zip file from the product rule or application, so you should have the product rule created in the application before you go for the jenkins export if you want to perform export using product rule.
Hope this answers your query and for more information about this automation you can have a look into this blog.
And I already have one. zip file of a product rule that I want to deploy to artifactory. Are you suggesting to create a fresh product rule and then use the above created Jenkins job to convert into zip (exporting product rule) ?
Create a Product rule then write a jenkins job with tasks export(creates zip file) and import(import zip file into target application).
Try to configure the application name and version instead of Product name and version in your jenkins job, then write export(creates zip file) and import(import zip file into target application) tasks.
If you already have the exported zip file then you can copy that into ARTIFACTS_DIR directory and write the import task in your jenkins job to perform the import into your target machine.