Why don't brushless motors "short"?
Those wires form coils, so are long.  Every bit of wire has some resistance, and all those bits of wire end to end result in a significant enough resistance to not look like a "short".

These wires shorted across a voltage source is exactly where the stall current of the motor comes from.  It is simply the voltage applied to the coils divided by their resistance.

When the motor is running, then another effect is present.  The motor actually acts like a generator so that spinning in the forward direction cause a voltage to be generated across the coils.  This voltage opposes that applied by the external power source.  The current thru the motor is therefore the power voltage minus this reverse EMF produced by the motor acting as a generator, and that result divided by the coil resistance.  The faster the motor spins, the less current, because a higher back EMF is subtracted from the driving voltage.

This back EMF effect also limits the top speed of the motor.  At some speed, the back EMF generated internally cancels the applied voltage, and nothing is left driving the motor.  Of course it wouldn't spin at that speed since nothing is driving it anymore, but it works at a little lower speed if nothing is loading the motor.