I'm not sure how the demo iOS player worked, but the main difficulty is that CDF relies on the Mathematica kernel, a very large and somewhat unwieldy piece of software. It has parts consisting of C, Java, and Wolfram Language code, and it would take ages to fully port. The Wolfram Cloud app avoids this problem by providing a lightweight frontend to a cloud-hosted version of the kernel, at the significant expense of speed. I don't know if work is still underway on a native CDF player, but for now it's probably just not possible.