Probably very similar to how lengths of cable are measured. It's generally pressed to a metal wheel with a flat outer diameter, and with reasonably appropriate accuracy in machining and such, length is measured with that - often with a counter (and reset button) attached to that wheel. Mostly just need to reasonably well press cable to the wheel as it's drawn across. Well, string would be fairly similar, reasonably well press string to metal wheel like that as the string is drawn across.

Could also do something like accurately measuring circumference of some suitably designed wheel/hub, running the string around that one full turn then off onto something else to be spooled (so it doesn't get fatter with string piling up), and carefully measure it's rotations (and start and end angle of rotation). Probably not too horribly complex to do something like that, and may not be as sophisticated, but may be a much easier set-up ... with a suitable wheel/hub and mounting, and string routing means and procedures.