Epic does not want to access Apple servers or content. Epic want right to have their own store that sell games for iOS.
Epic is saying Apple is does not allow anyone to compete with Apple by abusing their position as OS vendor to create illegal monopoly in app sale. Apple say it is not monopoly because iOS apps are not a market, but instead all software (regardless of operating system it run on) should be seen as a market.
If Apple win, it set legal precedence that it is legal for other company also. It will set a new standard for how software is sold in all future OS (maybe not include Linux that is free).