Yes, lasers can damage video cameras.
This is due to the very focussed rays. A video camera has a very sensitive sensor to transform the immitting photons to electronic impulses. Laser beams have a very high energy density in the point where they hit the camera sensor. The distance to the laser is a crucial factor: The farer away from the laser source, the less dangerous is it to film the laser show.
Using an optical zoom (or other lenses) increases the danger of damaging the camera sensor, as it focusses the beams even more to the sensor.
In professional laser shows, the laser operator normally specifies certain safety zones in the software to have the laser blanked off at the camera positions.
Do not film laser shows from very near distance!
Do not zoom into the laser beams!
See what happens if you zoom too close:
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Wow, what a beam!
Zooooom ... amazing close!
Oops, too close!