Not in the market of hardware, but in the market of software certainly. They control who gets to publish the apps, and as you can see, also who gets access to development resources for the platform. And while it’s not a neccessity for living, it is a neccessity for business for a lot of companies, or at least a large share of their revenue. That gives Apple massive leverage.
You don’t need to use Unreal Engine. It’s one of many tools out there. But if you want to develop an app for iPhones, you either work with Apple or you make some sort of side-loaded niche app, which most users won’t have access to. And even on Android, if you’re not on Play store, most users probably won’t bother. Your audience will be very limited
Remember when Microsoft wanted to get into the mobile OS market? That didn’t work even with their resources. Now they did make some mistakes, for sure, but they did identify their biggest weakness right away, which was access to applications, originally developed for other platforms. They tried to fix it with various grants and programs for developers, very generous ones. It never really worked.
I think ultimately the issue here is that they control the product AFTER you buy it, by ensuring it can’t be repaired or changed and that you don’t have full control over it.
I think there might be hope for you, as big companies generally don’t like loosing money. And blocking Unreal Engine means loosing money for them. So ultimately it might all be just a show, and they will quietly come to some sort of agreement or at least Apple will loosen it’s embargo.