Still no solution, but an update:
In order to identify the unknown audio device, I've installed Windows 10 in parallel.
The supplied Realtek driver did work in this case, the 9D70 device is "Intel(R) Smart Sound Technology Audio Controller".
Many other devices (SST OED-controller, Realtek High Definition Audio (SST), Intel SST, Intel Display Audio etc.) appeared too, but all of them are using the above controller.
Driver details on SST Controller reveal a list of driver files, most notably IntcAudioBus.sys (126.96.36.1990, Intel).
This driver is, however, not compatible with Win7 and I can't find a suitable version.
As mentioned before, manual installation (pointing to the .sys file directly) doesn't work.
Thank you for joining the Intel communities.
Unfortunately we don’t have records of the drivers for your system; the only driver that we can get for you is the graphics driver, any other driver and even the graphics driver needs to be provided by your system manufacturer.
Now, it is important to have in mind that using drivers from the Intel website not necessarily will work properly as branded computers are custom products that have proprietary designs and therefore they need proprietary drivers as well.
The best recommendation we can give you is to make sure you are using the latest drivers for your laptop from the Acer web site.
Here is a link for the Acer website where you can get support or contact Acer directly.
I did try the NUC version, unfortunately it doesn't contain the required HDASST / HDAudioBusDrv / IntcAudioBus.
Acer only offers Win10x64 drivers: their sound driver "Audio_Realtek_188.8.131.520_W10x64_A.zip" is the only package containing a HDASST folder and a working (Win10) driver for the audio controller - this folder is missing even in the latest official Realtek driver package.
As a side note, the version number (184.108.40.2060) in the above file name is exactly the version of IntcAudioBus.sys - obviously, it is the most critical component (Realtek driver itself is 220.127.116.1121).
Manual/forced installation of that sys-file in Win7x64 leads to a BSOD - not compatible indeed.
Seems a Win7 driver simply doesn't exist at all. Though I can hardly imagine that Win10 being the only Windows version usable with 6th gen Intel hardware can be intentional.
For everything else except sound I've found working drivers already.
Try this one: Download Audio: Realtek* ALC Audio Driver for Intel® NUC. Yes, it is also for the NUC, but is a newer version of the package.
My understanding is that the Intel High Definition Audio Controller (9D70) provides a significant portion of the overall solution, but relies on a separate Audio Codec device (and its driver) to complete the picture. Since the whole solution requires the driver for the Audio Codec device before it can operate at all, the drivers come with the Audio Codec driver.
Hope this helps,