Universal Android TV App for iOS

No, unfortunately not. I simply just gave up and bought a Nvidia Shield TV. Run's Kodi which is what your looking for by the way but is no longer available for iOS, plus your device needs to be JailBroken which as of right now, no iOS 9.2 solution has been introduced. It supports my TV's 4K resolution, I can control it remotely with my phone or tablet, I have a 4TB Lacie Cloud HD connected to, a 360 Amazon Webcam, USB replica game controllers for N64, SNES, Sega, DreamCast, PlayStation and even Pong Paddles. I can stream games via Nvidia's Grid gaming service, can play converted PC games like Doom 3, Portal, HalfLife, Halo, etc. and can even stream my games from my PC. I can RIP/Encode DVD's and BluRays with a connected drive, using a CUDA based encoder that utilizes the 256 CUDA core GPU found in the X1's SOC, I can encode a video 5x faster than a iPad Pro and any Intel GPU based laptop.

It's worth a look, the Apple TV was just simply to much of pain and missing to many features. Trust me, you will be a lot happier with something like the Shield TV, which is by far the best TV Set Box on the market today, it absolutely wipes the floor with Apple TV.

And if you find you don't like it, just install Linux on it and use it as desktop computer or buy 4 more and make a cluster out of them, mini render-farm. I made one from 5 Nvidia Jetson TX1 development boards, which are basically the same boards in the Shield TV.