In simple terms, a quick-shifter is a switch connected to the gearlever/linkage.
When you move the lever to change gear, it cuts the ignition spark to the plugs,( momentarily switching off the engine ), cutting the drive load on the gearbox and allows you to select the next gear. When the gear lever returns to the middle position, it re-instates the spark.
It saves the time it takes to pull in the clutch, shut the throttle, open the throttle and release the clutch again.
In clutchless changes, you take the load off the gearbox by closing the throttle.
I don't know about the ZZR1200, but ZZR1400's do not like a quickshifter fitted. The circlip retaining teeth on the secondary gearbox shaft break off, allowing the gears to have excess end float, causing difficulty in getting gears.
I, like you, have done clutchless changes for years just by closing the throttle, only on up changes, my bikes have always been fine.