In the US tethered pins with cords aren't really a thing, instead most bowling alleys use mechanical pinsetter machines. These machines are large, complex, and expensive (see here for a video on how they work:
https://www.youtube.com/watch?v=Iod6uwUGM2E ) which is why he's talking about the equipment being 70+ years old- with the revenues most bowling alleys make, it's not economical to replace a pinsetter instead of maintaining the current one. This also means that the alley needs to have a mechanic on staff to keep the pinsetter running smoothly.
The way the machines detect the pins is still fairly simple. The assembly that puts the pins into place moves down after the ball is thrown, and has sense switches above each pin that detect which pins are still standing.