No, we're talking about (up to) 4K content going out to an external 4K screen; that doesn't exist, which is why it is being rumored for this future apple TV.
I know, that's why the new AppleTV should have at least HDMI 2.0 and probably also HDCP 2.2.
However, I was strictly talking about the SoC capabilities. The A7 as well as the A8 can drive such resolutions perfectly fine already (because it can already decode 4K H.264 movies with up to 30fps and about 50mbps bitrate) and it also has to downscale that to the iPhone's native resolution, which means that an AppleTV with an A8 is more than capable to do it, because the A8 is even more powerful (4K up to 60fps and about 100mbps bitrate). The current AppleTV 3 uses an A5, so of course this doesn't currently work, even if there would be HDMI support.
Your iphone 6 is 1334x750, and the current iphone AV adapter only feeds a 1080p HDMI connection. It's not a stretch to render to that resolution, and the refresh rate adjusts to the native source rate. When the resolution is 4x the size, and the refresh rate is fixed by the screen, the processing load is seriously significant.
Current iPhone's are not resolution limited, they can support up to 4K easily with the A8, if such a screen would be available. Also, the iPhone AV adapter is totally different kind of hardware, which has it's own limitations (it has it's own, very weak 1080p H.264 encoding/decoding unit). The SoC is a lot more powerful than you might think. It's just that Apple limits it' capabilities to the outside world through it's APIs, like the H.265 support that is already included within the A8, but no one currently has access to it, excluding Apple.
Long story short:
If the new AppleTV uses at least an A8, it can drive a 4K display without any problems. An A8X would be even better of course. Maybe Apple will use their A8X salvage parts and disable the third core (like they did with the A5), so it has a dual-core A8X in the new AppleTV. I would actually prefer this over an A8, because the A8X has a lot more graphics performance, higher memory bandwidth and should also be pretty power-efficient when you disable it's third core.