There wasn't any computing involved. The video was recorded as a sampled analogue signal, with pits of varying length setting the "output voltage".
If you look at a Constant Angular Velocity disc you can actually see "spokes" radiating out from the centre, with two broad ones 180° apart. The narrow spokes are the horizontal sync pulses occuring every 0.576° - the disc rotates at 25 revs per second and each concentric track is one complete frame. The broader spokes are of course the vertical sync pulses and colour burst occurring every 1/50th of a second.
If you're in the US or Japan, these numbers are 30 revs per second, 0.686° and 1/60th of a second, because of the lower resolution video standard, but it doesn't look like Laserdisc was much of a "thing" in those countries.
Here in the UK, in the 1980s all the schools took part in a thing called "The Domesday Project" [1] - the name is a reference to The Domesday Book, a survey of England and Wales carried out in the 11th century by William the Conqueror.
The Domesday Discs were CAV Laserdiscs that were played in a special player with a SCSI interface, attached to a BBC Micro computer. Because each concentric track was a complete frame it was possible to get perfect still frame video by just keeping the head still, so you could look at photos of places all around the UK and read a bit of information about them genlocked over the top.