The more interesting questions is, why is Apple complying? Are they afraid that Amazon will retaliate by pulling their apps out of the App Store? If so, are they really just going to keep prioritizing big tech connections in favor of it's own customers?
The rule cited is so vague that even a basic paid browser app would break it. All the app does is augment data available from any web browser with other data.
> 5.2.2 Third-Party Sites/Services: If your app uses, accesses, monetizes access to, or displays content from a third-party service, ensure that you are specifically permitted to do so under the service’s terms of use. Authorization must be provided upon request.