That store (Ekoplaza) happens to be 5 minutes away from my house, so I rode by to check it out.
As you can see, the "aisle" (in what used to be a bike parking garage) is just a collection of foods packaged in glass, "bio-plastic" or nothing at all. That's not revolutionary.
What's worse, the "plastic free aisle" also has a "Bluewater" kiosk outside that is supposed to reduce the use of single-serve plastic bottles by giving you a place to fill your reusable (plastic or metal) bottle. Although this is a nice idea, I think that the kiosk probably represents a negative environmental impact, given Amsterdam's excellent tap water quality. It seems to be there as a giant advertisement for "buy our water filtering product."
Bottom line: The best way to reduce plastic use is to tax its source (oil, via a carbon tax). The best way to reduce pollution from plastic water bottles is to add deposits to their price, to pay for recycling and re-collection. After these simple actions, then you need to consider the total costs/benefits of switching to plastic from paper or glass. In many cases, plastic has a smaller environmental footprint than its "virtuous" replacement.