AVRDUDE does not recognize USBasp device
Found the solution, which is of course dead simple once you know...

In Zadig, you can select the driver. Default selected is (in my case) the WinUSB driver. When I select the libusb driver, and install that driver, it works like a charm.

Yeey. 



avrdude -vvv -c USBasp -p m32u4 -u -U flash:w:Duroduino.ino.hex:i

avrdude: Version 6.3, compiled on Feb 17 2016 at 09:25:53
         Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
         Copyright (c) 2007-2014 Joerg Wunsch

         System wide configuration file is "c:\_SVN\p(r)ins\Durocan\Deployment\avrdude.conf"

         Using Port                    : usb
         Using Programmer              : USBasp
avrdude: usbasp_open("usb")
avrdude: seen device from vendor -&gt;www.fischl.de&lt;-
avrdude: seen product -&gt;USBasp&lt;-
         AVR Part                      : ATmega32U4
         Chip Erase delay              : 9000 us
         PAGEL                         : PD7
         BS2                           : PA0
         RESET disposition             : dedicated
         RETRY pulse                   : SCK
         serial program mode           : yes
         parallel program mode         : yes
         Timeout                       : 200
         StabDelay                     : 100
         CmdexeDelay                   : 25
         SyncLoops                     : 32
         ByteDelay                     : 0
         PollIndex                     : 3
         PollValue                     : 0x53
         Memory Detail                 :