KGB, please read the entirety of this post before commenting on it.
The entire platform uses multiple lasers. The first are a set of non-visible, low-yield lasers which are pointed at the target used to acquire and gather the range, bearing, etc. of the targeted missile. Then the main COIL laser is fired, with the intent to kill the missile. All the lasers involved are non-visible, so they won't blind sensors operating in the visual spectrum. The targeting laser and the main laser are probably operating on different wavelengths and would not interfere with each other.
It isn't Star Wars with neat little packets of glowing lasers. Its a long, continuous invisible beam.
I'd also presume that radar is also used to track the missile, although I don't know it if provides targeting data.
(
Laser Weapon Knocks Down Missile Off Calif Coast - CBS News)
Please remember that enough light has mass too. The physical energy hitting the missle from a 5 meg laser is equivalent to the impact of a World War Two vintage 75mm shell. The amount of weight of electrons is miniscule, but they are moving at the speed of light, and energy increases to the square of the increase in velocity. Quite simply, the thing could be a flying mirror, and the laser's energy would simply batter a hole in it.