How to measure power consumption of pulsed DC motor correctly?
Average current does take both the ON and OFF current into account ... but if there is OFF current, it flows during the time when you are supplying 0V not 24V.
Multiplying by the duty cycle correctly accounts for this variation in the supply voltage.
An example where this is accurate is PWM switching a voltage source via an inductor, in other words, a buck convertor.
It's probably the most reasonably accurate technique back in the days of electric typewriters or daisywheel printers when that letter was written; nowadays you'd sample both current and voltage well above the Nyquist frequency and compute an accurate average power using DSP.