How can a multimeter measure current while being parallel to the element
This is the paragraph in question: 


  For analog current ranges, matched low-resistance shunts are connected in parallel with the meter movement to divert most of the current around the coil. Again for the case of a hypothetical 1 mA, 500 Ω movement on a 1 A range, the shunt resistance would be just over 0.5 Ω.


They are describing the internal workings of the meter. You always connect the meter itself in series with the current you want to measure so all the current goes through the meter. 

Inside the meter there will be a shunt resistor and a voltmeter, at least in the case of digital meters. Analog meters are inherently current meters, but they are made to deflect fully with a very small current, so the shunt divides the current allowing a fixed portion to go through the meter movement (except perhaps on the lowest DC current range). A typical analog multimeter, more realistically, would have a movement that would deflect fully with some tens of uA. The Sanwa meter shown has a sensitivity of 20,000\$\Omega\$/V so it is a 50uA (full scale) movement. You can also see that the lowest DC current range is 50uA full scale. 





At some point you might wonder how a shunt divides current in the case where the underlying meter is a D'Arsonval moving coil movement- ideally, putting a shunt resistor in parallel would have no effect (look at the current divider equation), but real meter movements have significant internal resistance, so you would shunt the movement with a fraction of that resistance, and likely you would add some resistance on top of the copper resistance. And if that series resistance you added happened to have a slight negative temperature coefficient it might compensate for the positive temperature coefficient of the copper coil.