If an AVR is to play Zone 2 from sources that are only connected digitally, it must have a D-A converter for the main zone and a D-A converter for the second zone. That would cost money, and apparently none of them have even considered for a blinkin' moment spending money on this.
It's not hard to conceive of if you describe it slightly differently: You say
Does the RXA820 need an analog feed in combination with the HDMI input to get sound to zone 2?
and
From looking at the back of the 820 I need to tell it to link one of the two analog inputs to the HDMI input to possibly work.
The first slightly different way to think of this is that Zone 2 is an analog system. And there's your answer.
The second is that you don't link one of the analog inputs to the HDMI input but instead you link one of the analog inputs to a device that uses an HDMI input. The way you're expressing it, HDMI has the DVD input and you need to link the analog input to the HDMI. Instead, it's that the DVD has an HDMI input and you need to link an analog input to DVD, too.