"That being said, I explicitly give permission for anyone to use, modify, and distribute my original code for this project without fear of legal consequences —

"That being said, I explicitly give permission for anyone to use, modify, and distribute my original code for this project without fear of legal consequences — unless you plan to submit your app to Apple’s App Store, in which case written permission from me is explicitly required." Emphasis mine. The author is giving permission to use their original code but doesn't re-license anyone else's code. They're explicitly offering their own code under a dual license.