Download driver in ZIP format from -NEW- 22.214.171.12453: Intel® Graphics Driver for Windows® 7*/8.1*/10 [3rd Generation]
Install the driver via "have disk method" as described at:
(ignore prolog about MS surface)
Open device manager again, check for yellow bangs (gelbes Dreieck mit Ausrufezeichen), especially Intel system devices.
If you find sth. like that you would need to install Chipset driver in first place.
There aren't any exclamation marks in the device list, but nevertheless the problems seems to be resolved. After many attempts of installation (which all ended in an error message), the version number magically changed, so the installation seems to have worked spite the error messages. Thanks again for the quick help.