Yes, what Olof Hedman wrote.
"App" does not refer exclusively to mobile devices. It may have become a popular term in that domain, but it is in no way exclusive.
Re-reading my post:
Both. I spent several years developing objects for the Sims Store. Limiting yourself to just in-app purchase or to just web purchase is unnecessary. For only a small amount of extra work you can do both. Well, usually. It can be difficult on mobile because of requirements to go through their store and the inability to issue keys. But you didn't specify mobile in your question.
If you use the typical license agreement with the companies, which almost all developers must do, then you are bound to go through their payment processing system and follow their rules.
I have never seen any inapps or purchases in an iOS app that was not handled ingame from the iTunes store, can you give an example of this?
Very large companies, such as EA and Ubisoft, are able to negotiate their own contracts with Apple.
As part of those contract negotiations, sometimes in order to get high profile applications Apple is willing to make concessions that allow the customer to do some transactions through the company's own payment portal, like Origin or Uplay.
These are not part of the regular everyday agreements you click through on the website or the standard developer account. These are large, multimillion dollar contracts being negotiated by groups of laywers and well-paid executives at both companies.
If you are going through the normal channels because you are a normal group working on a normal product, Apple and Google demand you go through their payment processors for everything.