In fact Sky Go via HDMI currently works fine on my other Android products and my Xbox which is pure HDMI. But perhaps this is one motivation to move to an app based approach for PC's.
Nonetheless, the German and presumably other European version's of the Sky Go Android app work perfectly (well with a little bit of fiddling for the install) on the Firestick so its does not really seem to be a technical HDMI issue as opposed to one of deliberatley restricting use.
I still think that Sky are missing a trick here. Build it and we will come!