How I found it
I went to the product page on the LogiLink website, clicked on “Downloads”, then on the link to the driver which sent me to a 404 page on 2direct.de.
I then searched for the product directly on the 2direct.de website, found it here, clicked on “Downloads”, then on “Treiber AU0033” (Treiber is German for driver), which led to a PDF document that in turn contained the link to the actual driver ZIP file (which is hosted on the LogiLink website where I started).
Note if you’re reinstalling the driver
You can find an uninstaller under “Logilink AU0033 8x seriell\CD\Driver\Windows\64X\9710_7840_QUADPORT_MSUninst.exe”, running this before the installer fixed a problem on my system where only half of the ports would appear.