Special HDMI cable for Apple TV?
There is no reason why it wouldn't work. In fact I use even cheaper (but shorter) cables myself and they work fine. For reference, I paid €0.75 a piece for a couple of 0.75m HDMI cables with a local online cable shop, and they work fine for 1080p video.

I'd advise to not succumb to the "gold or silver plated" marketing nonsense or the overpriced "premium" HDMI cables, as even the cheap cables transport your binary 1s and 0s just fine.