A dedicated device means everyone in the household can use it without the friction of having to help everyone find the app and register with the same account.
People without phones (like kids) can use it.
It's designed to sit on the kitchen counter or hooked on to something. That physical presence reminds you to use it when you're in the kitchen, where an app buried on the last page of the home screen is easy to forget.
The camera-based barcode scanners like the one built into the Amazon mobile app are significantly more difficult to use than laser scanners. In a grocery shopping context, shoppers will purchase dozens of different products and every bit of additional frustration and delay matters.
One issue with the website: the hero image is really bad. The background is blurred out so there's no context and there are no other objects in the frame so I have no sense of scale. If there was like an apple next to it or something, and you could see it was in a kitchen, that would be so much better.