BTW: Why is the ammunition for these systems still on chains -- opposed to "just" shovelling it into some kind of funnel?
Chainguns generally depend upon an external drive to pull ammunition through a gun -- whether a round in the chamber has fired or not, it will be extracted and a new one put in its place. As I understand it, this is the primary difference between chainguns and belt-fed guns (which use part of the energy expended by the cartridge to cycle the weapon and feed the belt) -- reliability.
It doesn’t have much to do with how the ammo is loaded. Also most auto cannons today even the high fire rate ones that are used for CIWS and AA aren’t chain guns.
An air burst round doesn’t require the system stay pointed as a single target, whereas a laser needs a few seconds on target.
At speed-of-sound, a munition moves at about 0.2 miles per second, or about a mile in the engagement time. Which caps the number of targets it can intercept to a handful.
That's cute - but we aren't firing airguns at these things. A CIWS (the R2D2 looking missile defense cannons) fires its rounds with a velocity of around 3600ft/s, or 3.5x what you seem to be thinking.
Faster munitions means that the laser can intercept proportionally fewer targets — which is why it’s a question of if lasers can fend off swarms the way gun based solutions can.