AIUI and IIRC, iSH implements just enough of an x86 emulator to be able to interpret x86 binaries and JIT "compile" them to a series of function calls rather than directly to native machine code, and it implements enough of the x86 Linux ABI to be able to run most binaries. In short, it's effectively treating x86 machine code as a scripting language, and Apple does allow scripting languages (e.g. Python) on the App Store.

The iSH team did run into some friction with Apple over the fact that the built-in filesystem image is Alpine and thus includes a package manager, but apparently they were able to resolve that situation in a way that allowed them to keep `apk` in the built-in filesystem image: https://ish.app/blog/app-store-removal