I can think of a couple of scenarios that might fit what we know so far:
1) Apple might simply declare that they want 30% of all in-app purchases. Amazon will likely freak out. This, to me, would seem to be a seriously dangerous move on Apple's part.
2) Apple may drop the 30% cut entirely on in-app purchases. That'd be pretty disruptive but aside from adding a technical hoop to jump through for content providers to link content with Apple's in-app purchasing system, I don't think they would be quite so upset about it since they wouldn't really be losing money on each transaction. Of course this is still pretty harsh on Apple's part, IMO, but it's better than #1.
3) Apple simply requires developers to link purchased digital content with an Apple ID via the in-app purchasing system, but not necessarily requiring that Apple be used for the actual money transfer itself. The purpose of this would likely be to ensure that purchased digital goods are always linked to an Apple ID - even if they were purchased externally. If that's the case, then this is much less of a big deal, IMO, and a huge win for users. For instance, if you restored your device, you could be assured that all your digital content you bought via the Kindle app itself would be restored with a single tap - no need to login to Amazon again or anything like that. Thus Apple can help better ensure that the user will actually get their content back when the device restores which is required of all other in-app purchased content using the in-app purchase API.