It sends a message - this is a warning shot. If things don't change, another extended boycott can be organised. These people think quarterly, 7 days isn't insignificant on that time horizon.
The first day is the hardest. You NEED that thing that Amazon has made easy for you to get with just a click from your couch. You drag yourself off the couch grumbling and get on the bus/on the bike/in your car (if you have to) and go out and buy something just as good (if not better), from the local store. You repeat this a few times. By day 7, you realise...you can buy the stuff locally, not supporting a knee-bending billionaire, and the world hasn't ended. Even if you still buy things you just can't find from Amazon after the 7 day boycott, you find many things you can buy locally without funding Nazis. Your total sales goes down, and you're more inclined to shut down Amazon Prime. Eventually, you are only using Amazon as a last resort.
And that's how you go from a 7 day boycott to changing your life. ;)