I've travelled to Vietnam many times with a business visa. I am certain they keep a record of your visa on their system in correlation to your passport number.
Prior to your departure to Vietnam you should have received a visa approval letter (sample below) stating that your Visa is waiting for you at your port of arrival. This document has your DOB Full, name, Passport number and nationality. The form is electronic and thereby would be entered in a database of some sort where immigration and visa officers can cross check.
When you pass passport control, the officer will scan your passport, check your visa and cross check it with the monitor in front of them.
This is a sample letter: