No, this is likely part one of an overall strategy.
If you noticed the blurb, they've been "working with" Amazon to tackle the issue. However Amazon is unable or unwilling or a combination of both to give them the tools they've been asking for. I'm guessing they'd want something like YouTube's ContentID to flag things. Of course, providing such a tool would be against Amazon's M.O. since it would likely cut into sales to a noticeable degree. Thus the move to get out of Amazon completely.
Next step is likely threatening letters between law firms. The content of which is something along the lines of "so-and-so seller on your marketplace is selling known bogus goods that infringe on our trademarks/trade secrets/fill-in-the-blank. we demand you remove them or face legal consequences". After a few months of this, either Amazon will start policing themselves better, producing the tools needed to remove the sellers OR Amazon will continue to not care. Either way, Birkenstock wins.
Either Birkenstock gets the tools needed to flag sales and they come back to Amazon OR they get to drag Amazon into court for facilitating trademark infringement. Birkenstock is going to have a nice paper trail of correspondence showing that Amazon doesn't care and plenty of other sellers who've been pushed out of the marketplace.