Yes! You can export each record's attachments in the Subfolder by just turning Toggles.
- Go to the Mass File Download App.
- Click on the About Mass File Download Tab scroll down and Check File Download Configuration.
- Now tune on the Download Files in ZIP format toggle and Download Zip of Files in SubFolders toggle.
- And hit the Save Button.
PS: View Mass File Download, Salesforce file download app on Salesforce AppExchange: https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3A00000EcsAOUAZ