Ye olde ammeters were secretly voltmeters with a low-value but high-precision shunt resistor in series with the circuit to be measured.
Current passing through the resistor causes a tiny voltage drop, which is measured by the meter. As the voltage is proportional to the current, the scale painted on the cardboard behind the needle did the actual conversion.
In the author's setup the fuse takes the shunt's place; its resistance is apparently a known value that can be gathered from a datasheet.
The absolute current value probably doesn't matter - in fact I very much doubt a hobbyist-level multimeter is even capable of accurately measuring the (fractions of?) millivolts across a fuse.
It's more important as a boolean signal - "is there current being drawn on this fuse?", and then usually even those fractions of millivolts will generally be enough to make your el-cheapo multimeter register 1mV and tell you something is drawing current, where as a fuse with no voltage drop across it at all will reliably show 0mV (just like it would if the probes were shorted) on even a cheap meter.
Same idea really, just that you have to bother disconnecting something and try one by one vs just measuring it fuse by fuse.
Other method is getting DC clamp meter with low range (say 2A). Then just clamp in on wires. Bit fiddly as they work on magnetic field so they need to be reset before measure (And can work as compass in a pinch...)
How does this compare with the way presented in the article based on measuring resistive voltage drop across each fuse in turn?