The machine has a wheel that rotates at a fixed speed. By imaging a pattern through the camera, you can determine the shutter speed. The video shows a high-speed video of the shutter function, which is well worth watching, and also explains exactly how the rotating disc combined with the rotating shutter allows the metering.
The marks on the rotating drum move at a precise speed adjusted with a stroboscope. The rolling shutter on the camera shows each horizontal bar as a diagonal line and the exact pattern will show the exact speed. The lines are slightly curved due to the characteristics of the shutter spring.
Honestly, this is one of those things that is probably of zero practical value today. But we never fail to marvel at the ingenuity of engineers who had no access to modern technology. Or materials for that matter.
Thanks to (zit) for the tip!