An Amazon account isn't required to use DiscovR if you are simply streaming content over Bluetooth or Spotify Connect. However, it will allow you to get the most out of your speaker and provide access to a wider range of Alexa supported features, including voice control and Quick Corners.
If you already have an Amazon account, simply enter your log-in details when prompted during the product setup. If you don't currently have an account, you will be prompted to register for one in the Pure Home app.