I installed Debian Stretch (Kernel 4.8.0-1) multi-arch net-inst successfully to the eMMC, with Grub, and dual-boot to the original OS (where the sound does work).
Well, with half the peripherals. This question is about the HDMI-Sound. I tried:
$ aplay -l
aplay: device_list:268: no soundcards found...
$ lspci
... Z36xxx/Z37xxx Series Graphics & Display (rev 0f)
$ xrandr --output HDMI-1 --set "audio" "on"
(Screen flashes once, but no change apart from `xrandr -q --props` output)
# dmesg | grep -iE 'audio|so?u?nd|sst|pcm|hda|hdmi'
intel_sst_acpi 800860F28:00: no matching machine driver found
# dpkg -l | grep -iE 'intel|nonfree' | awk '{printf $2" "}'
firmware-intel-sound firmware-linux-nonfree firmware-misc-nonfree i965-va-driver
intel-microcode iucode-tool libdrm-intel xserver-xorg-video-intel
Grepping -iE 'audio|sound|sst|0F28' my decompiled ACPI DSDT like described here resulted in 5 blocks of 3 lines with "Intel Audio" devices, including some with "HAD0F28 Intel HDMI Audio driver". The others are 80860F28, ADMA0F28, TIMC0F28, AMCR0F28. Curiously, there also were 4 lines like 10EC5640 Realtek I2S Audio Codec.
This is of these "HDMI Compute Stick Clones". Mine is from CSL, called "PC on a Stick", but there are many different re-branders of the same same Intel Bay Trail Quad-Core SOC platform. Mine is the fan-less variant without the separate audio-jack. This is one of those "32Bit UEFI with a 64Bit Processor" beasts.
There is a dsdt acpi patch and a kernel patch from early 2015 floating around for a similar model, but I have not found out, if they apply to me, and/or whether they are already applied. (My UEFI Date is 09/2016, and my kernel is 4.8)
Another similar device seems to be the "Meegopad m1", and the ODM name seems to be "Quanta NH1". Mine has a problematic Broadcom Wifi brcmfmac43430 though.
How get I get the sound to work, or where do I go from here?