No, the stylus only works with the iPad Pro and new with the iPad 9.7" 2018 release.

I don't quite understand the designations for compatibility: is the pen also compatible with the "normal", i.e. not mini Ipad of the 5th generation 2017?

It will work with ipad 6th and 7th gen - and the latest, ipad air, ipad pro 9,7" and 10,5" (but not ipad pro 11" or 12.9" 2018 with usb-c - they take the apple pencil 2) - and it will work with the latest (current ipad mini - but no ipad mini before that. And no iphone has pencil support.

Should actually. If not, just return it, Digitec is always very accommodating!