Most low-end AVRs don't allow downmixing of audio. You can generally push 2ch PCM from a digital source to a second zone, you just cant push 5ch+ into those additional zones. Party mode on Yamahas converts the primary zone audio into 2ch PCM, which is what allows it to push the main zone into additional zones regardless of the input type. Denons are similar, without the benefit of that party mode conversion into 2ch PCM. If the audio into the main zone is 2ch PCM and you set the second zone to Source as the input, it will push that audio in zone 2.
Internal streaming on AVRs can push to zone 2 while the main zone pushes a digital source. That's the best way to run a surround and zone 2 setup. Primary zone streams audio from an input (roku, chromecast, whatever) and zone 2 pushes the internal streamer (Heos or musiccast). That way you can run two different audio sources without having to nug with having to lose the main zone surround. If you want to sync the music across the main zone and zone 2, you just set the main zone to the internal streamer as well.
Higher end AVRs will downmix audio, which allows surround in the main zone and stereo in the secondary zone. They are usually double or more in price of the low-end AVRs though, and again, if you want to push more than 2 zones, a true DA solution is probably the better way to go.
There are audio extractors that will peel out audio from an HDMI signal and downmix it to 2ch PCM. The problem with that is audio delay between a display and a zone. A display has to process an HDMI signal into whatever it puts on the screen, and its usually slower than an AVR. Its the same problem as using the 2ch output on a cable or DTV box into the AVR or DA as a source for zone 2. The audio will be ahead of the display's audio that was processed slower, resulting in an echo effect if the speakers are in or near the same space. You're better off using an audio balun pulling audio from the display into the AVR or DA system so the audio is in sync.