Apple have never shown any interest in the videogames market, aside from providing the app store where games were a popular segment. I would expect a new apple TV to continue the trend of allowing 3rd parties to provide gaming content, but never risking their own money and reputation on that venture.
No, no it wouldn't.
If Apple made a video games console that was compatible with all of the Apple products currently available (iPod, iPhone, iPad and Mac) then Microsoft, Nintendo and Sony would be up “Shit Creek.” If Apple announced the iGame console at E3 this would certainly put a spoke in the wheel of Microsoft and Sony’s new console plans. Gamers who have claimed “I’ll pass on the Wii U and wait for the real next gen” might have to buy an Apple console as the PS4 could be PS4-cked and the Xbox Next could end up the Xbox Not.