Objective-C is designed in such a way that, generally speaking, anything you can do with Objective-C syntax can also be done with a simple C function call to one of the Objective-C runtime functions. So you can write an entire iOS app in pure C. However, the Objective-C stuff is a lot more pleasant to use if you use the syntax for it.

As others have mentioned, for something like a simple game (rather than a normal GUI application), SDL offers a convenient wrapper that allows you to avoid touching anything Objective-C-related yourself, so you could write an entire app using only the SDL API, which is pure C. A nice bonus of that approach is that it would then work on other platforms with zero code changes.

Another source of C wrappers is Apple themselves, as iOS has a number of C interfaces like CoreFoundation that reduce how much Objective-C stuff you have to directly interact with, but there's nothing like that for UIKit, and every iOS app has to use UIKit at least a little.