Additionally, movie rentals are already covered by a prior agreement. The article you mention even says that Canal+ and other video services were already using this which is an option where you can allow purchases tied to an existing subscription payment method if you also allow for those purchases in the iTunes Store and integration into the Apple TV app.
There was no special deal for Amazon and trying to present it that way, is, imo, disingenuous. How can it be a special deal for Amazon if it existed prior to Amazon's app changes and other platforms were already making use of it?
Again, I have no idea what is possible on the Apple version, but I have subscriptions on other apps that go through the play store payment system. I'm not an expert on app store policies for payments, but I don't use any other apps that have subscription payment that don't go through the play store. I have a LastPass subscription which I purchased through their website, specifically because you have to go through the play store if you get it through the app.
On iOS though, apps need to use Apple's payment system for any digital good. Unless you're an Amazon Prime member renting a video.
All of this is described clearly in their information. [1]
"3.1.3(a) “Reader” Apps: Apps may allow a user to access previously purchased content or content subscriptions (specifically: magazines, newspapers, books, audio, music, and video). Reader apps may offer account creation for free tiers, and account management functionality for existing customers." [2]
Additionally, Apple also allow small business at 15%.
"Keep 70% of your sales proceeds (85% if you’re enrolled in the App Store Small Business Program) and 85% for qualifying subscriptions." [3]
[1] https://www.apple.com/app-store/
[2] https://developer.apple.com/app-store/review/guidelines/
Even if there was something very specific about Amazon's implementation that allowed them to bypass the rule—at what point is it fair to acknowledge the rule was specially crafted for Amazon? What if the policy had an exemption for "Companies that begin with 'A' and end with 'zon'"?
Buying/renting you can go via their site and I bet they prefer that for at least Google. They get all that customer info and no cut needed.
Any previously purchased items are available on the apps it is just in-app purchasing is usually turned off to prevent the iOS 15% cut for "reader" apps. They could have it on and available to use Apple's Appstore to rent/purchase but the in-app purchasing fees apply 15%/30% depending on the content and app classification.
Pretty easy to just purchase online and then watch in the app.
Games will always be 30% most likely because iOS is a gaming platform as well and that matches other gaming store cuts.
Even Tencent was 55% at one point for MyApp, they came down to 30% inline with other markets in 2019. Tencent MyApp is a competitor to Appstore in China, both companies make about $16B on their stores in revenues. If anything Apple/Google/Steam/etc all forced Tencent MyApp to come down to 30% from 55%. So things could be worse. Cuts prior to app stores were in the 60-70% range for gaming which was absurd.
Epic Game store is 12% (was previously 30% but they lowered to compete on price) which Tim Sweeney has said profitability is around 7-8% but they only allow in games that you have a deal with them. They don't allow just any game to be sold which adds lots of additional cost. Apple, Google, Steam etc all allow in any game which is good as long as it meets their ToS. Mobile really opened up gaming markets and that is industry standard now. Apple/Google even forced Steam to open up about 5 years after the mobile stores appeared.
My guess is break even for stores is about 10-15% if you have a more open market for all, part of that is keeping the stores/games secure from malware and payment info protected. That is why Apple was willing to go to 15% for small business and does for "reader" apps. They aren't making a ton of profit on those.