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.
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.