If you embark in Düsseldorf, it means you are already in the Schengen area (and since you don't have a short stay visa, you presumably have some other legal title to be there like a German residence permit). You won't leave the area before Zurich.
In most cases, you won't see any border guard before you go to the non-Schengen part of Zurich airport and you will in any case be free to leave the airport and do whatever you want. It's only when you go to catch your Vietnam-bound plane that you will be stamped out.
If you are coming from somewhere else, say London-Düsseldorf-Zurich-Vietnam, then you definitely need a Schengen visa for this transit, not merely to see the city in Zurich but also to be allowed to board your plane and catch the Düsseldorf-Zurich leg.
Either way, if you are able to follow this itinerary, you won't have any problem leaving the airport in Zurich.