The new Apple TV Remote app with Siri features and support for controlling games on the fourth-generation Apple TV via tilt controls on your iPhone is now available for download on the App Store. Formally announced at WWDC in June 2016, the app used to be available as a developer-only preview, but now everyone can download it from the App Store. The new app doesn't replace the old one, which is still available on the App Store.
Both apps support the second, third and fourth-generation Apple TV, but only the new one packs in full support for Siri and tilt-based gaming on the new Apple TV.