On a snowboard there is no such thing as the "Pizza" formation you saw beginner skiers use. On a snowboard you stop by using your edges to turn the board against the slope. By turning the board against the slope, the board is no longer aimed downhill and gradually loses speed. By making turns on a snowboard, you are constantly checking your speed each time the board veers away from the downhill line.
So yes, "zig-zagging" or linking turns are what slows you down. One thing that's for sure with a snowboard, is that if you point the thing downhill and don't turn, it's going to keep going until you hit something.
PowderHound and TreeNinja