When you stick a DVD into a BD player, the content is still 480p. Doesn't matter how much lipstick your BD player tries to put on it, it's still a pig.
Do you now understand it?
None of them are going to be even remotely close to what you can get with a dedicated box, not even maybe.
Thank you for sharing that you don't understand the issue of content vs. hardware outputs.
Your extensive development experience will of course differ to mine, but in my time developing for iOS devices I have learned that they are more than capable of outputting a game at 1080p.
Will they always? of course not. Do the Xbone and PS4 always output 1080p? Hells NO. Did the PS3 and Xbox 360, which the ATV is closer in power to, output 1080p often? No, hardly ever.
No-one is suggesting that an A8 powered Apple device is in any way going to challenge the current crop of consoles on a visual level, just not possible in any way shape or form. But the A8 is still an extremely capable chip that punches well above it's weight, it's not only a strong number cruncher, it has a relatively good GPU for such a small packaged device.
Given the right content, visual style, and a careful and considered approach to development and particularly rendering optimisation, outputting any type of game on an iOS, or TVos device at a native 1080p is not only theoretically possible. It's in fact a reality.
You don't have to take anyones word for it. Even without development knowledge, or knowing a single line of Objective-C or Swift. You can download both 2D and 3D sample apps direct from Apple, fire them up in Xcode and run them on your device. Then you can play about with some numbers and find that rendering well above 1080p is a reality.