The eagle eyed among you might spot there is no 'boost' circuit!!!
The pi zero is actually quite tolerant, you dont actually need to feed it the full 5v to make it work. The main core of the pi runs on lower voltages, so the majority of it will happily run as low as 3v (i have heard it will run lower, but li-po protection kicks in before we get there), the only real need for the 5v on the pi is USB peripherals, which most will be ok with 3v too!!
Therefore the battery (4.2v-3v) is piped straight into the 5v line on the pi, cutting a boost circuit out of the mix, keeping the power usage below 250mah