In having App Store as the only way to install common apps for their devices.
That doesn't seem like a monopoly to me. Apple has huge competition on the mobile market. Windows Phone 8 only had Microsoft's own app store, was that a monopoly with its <5% market share? I think not.
That sounds like an argument that "every single current game console and almost all other modern devices with app support" are maintaining monopolies on app distribution on their platform, what's your point? Epic Games is not obligated in any way to sue every company breaking the law just because they chose to sue one that is.
I can see the pragmatic sense in that argument, but I'm pessimistic and see it more as Tim trying to avoid destroying a relationship with strategically critical partners while achieving new strategic goals on mobile. Trying to have his cake and eat it too.
He's also allowed to believe that there is a stronger case against Apple and sue them first, and then sue the other people later if he wins the first suit convincingly, which is what I personally suspect is going to happen.