Yes, AM is amplitude modulation.

But in this case, the transfer isn't analog data with a specific amplitude representing a specific signal value.

It's enough to have a comparator that detects if the demodulated signal is stronger than a reference or not. The time code information is sent at a very low baudrate and with a format to make it easy to implement in a tiny microprocessor with a minimum of external hardware. You don't want battery-consuming extras in a wall clock or even wristwatch that is expected to have 1-5 years of battery life.