The way I understand it, the underlying complaint is that Apple is somehow "tying" IAP to iOS. "Tying" can be an antitrust violation and AFAIK it doesn't require the existence of a monopoly, only the existence of market power, which Apple definitely has.
I'm not sure why they are using the "monopoly within iOS" angle, I don't think it has any chance of succeeding unless it's some sort of PR way to present the "tying" argument, which will be IMHO the fundamental one.
I am also not sure whether the "tying" argument will fly, but it seems to me at least plausible whereas the "monopoly within iOS" is not.
A smaller market where monopoly in fact is not established through anti-competitive conduct is not illegal. However, Apple's App Store monopoly is established through anti-competitive conduct (bundling App Store with iOS, preventing users from using anything else). Apple's App Store monopoly would be legal only if iOS users had the opportunity to use something else but willingly chose to use App Store.
When a seller requires buyers to purchase a second product or service as a condition of obtaining a first product...
www.businessjustice.com
Offering products together as part of a package can benefit consumers who like the convenience of buying several items at the same time.
www.ftc.gov
"Proving market power isn’t typically required for practices considered per se antitrust violations, but it is for tying." So if they can't show that Apple is a monopoly, they don't have a leg to stand on.
I don't think the claim that this is illegal tying is going to get very far. They don't seem like separate products (buying apps, buying features?). You aren't forced to use IAP. Apple isn't using this to prevent Epic from competing, only to protect the user experience on the Apple platform. Epic has plenty of other routes to market.
And, as
@cmaier points out, there is precedent stating that you can't have a monopoly in your own product. This actually references back to an older suit against Apple by Psystar concerning Mac OS. A suit Apple won.
But winning the suit isn't really what they're after here. They're slinging mud, plain and simple. They're trying to build a narrative of Apple as the oppressor. They're hoping that by going after Apple's image, they'll force Apple into a more defensive posture. I don't see that happening either.
Apple seems to know exactly what the rules are, and they seem to know they're playing inside of them. I think that's a lot of the reason for how they deal with Amazon and Spotify-- they know that there is much greater risk of getting called out for using whatever market power they have in smartphones to gain market power in music or video. Again, I don't see Apple as a monopoly of anything right now, so I don't think there's much risk in music or video, but I could imagine Apple has aspirations to dominate a few of those eventually. Either way, that's not the problem with Epic, though.