How does a timing light detect the electricity in the plug wire?

A timing light works like a camera flash.

Inside the timing light there is a section that steps up battery voltage. That high voltage is applied across a gas discharge tube bulb filled with xenon gas. The tube is long enough that the high voltage won't arc over.

The pickup detects when the plug fires in an inductive fashion. That inductive kick so to speak is channeled to a coil wrapped around the bulb. When that coil becomes energized it ionizes the gas inside the bulb.

The ionized gas is conductive and the high voltage discharges across the bulb. In this case a flash. When the ignition event is over the ionizing effects of the coil subside. This intern causes the arc in the bulb to collapse.

A timing light could be used in a comparative manner across all the cylinders but not in an absolute manner.

Most timing lights have a magnetic pickup that will 'detect' current flowing through the spark plug wire. This triggers the strobe to flash. The signal is not amplified, it closes a switch. I do not think the brightness of the light is dependent upon how much current flows through as the light is powered from the battery. I believe the flash is less bright because it is being turned on/off faster.

You can see a misfire with a timing light when the light does not light when it should. You will get used to the gap of time between when it lights. If you see a double size gap, then the plug did not ignite for whatever reason. I don't look directly into the light, I just shine it at whatever so I can see the flashes.