First, you might ask the manufacturer if they have a LabVIEW driver already written for you. If so, that will save you time.
Since the computer is thinking it's talking to the multimeter through a serial port, I think you can ignore the tutorial on USB.
You do want to use VISA, though. Look at the Measurements Manual for some guidance about how to get started with VISA.
Basically, you want to use the functions "VISA Configure Serial Port" and "VISA Write" and "VISA Read".
Good luck getting started.
Brian