This was gone through ad infinitum just like the German VAT obligation a few months ago and was also covered by another vague Amazon news announcement. The upshot of it all is as Clearanceshed has indicated. If you sell on a foreign (To Germany) ecommerce platform - whether that be a marketplace like Amazon or ebay or your own website - you are not obliged to register under the German packaging law. - unless you store your goods within Germany awaiting sales to German buyers.
The German buyer who purchases from a foreign website becomes the importer of record and therefore is responsible for all liabilities be they import duty, VAT or in this case packaging (Although the packaging law is not applied to individual purchasers).