At a high-level, there isn’t much strategic difference between an original content TV service and a games service. You just need leadership with good taste to hunt out games, and sign the exclusivity deals. One distinction is that modern TV production can be expensive but the budgets of AAA console titles can be even bigger than TV.
Apple has deep pockets but even they will be hesitant dropping three hundred million dollars on a single game. You have to aim your sights slightly lower; you can certainly make visually rich and engaging mobile titles with much less financial backing.
You could even make a service with zero exclusives and instead push discovery of what’s already there. I can imagine a compelling discovery/rental proposition. What if you paid a dollar a week, and you can play any game featured in the “Games We Love” section of the App Store. The titles appear automatically in a special folder on your iOS’s home screen and it continuously refreshes. No freemium games, full proper games. When the title goes out of rotation, you can choose to buy it to keep, at a reduced price. I think an idea along those lines could have legs. It brings discovery outside of the App Store app, and feels like value of money to boot. A similar model could be rolled out for apps too.