Epic is fine with the appstore, but it wants to handle it's own in-app payments. You can have an app store with a separate in app payments; Uber does for example. Epic says as much in it's argument for a preliminary injunction.*
Stadia is actually more of an existential issue than Epic because they want to run unapproved games.
* https://cdn2.unrealengine.com/epic-v-apple-8-17-20-768927327...