There is no error in the excerpt in question.
Current flows thru the resistor. Ideal conductors remain neutral. However, there will be charges in the insulating medium attracted and surrounding the conductors from the Electric field.
The current would simply be measured across resistance as I=V/R.
Since all conducting wires also have a dielectric which includes air , two isolated wires in close proximity will always have a capacitance between them and can transfer charges when the electric field is rapidly changing Ic = C*dV/dt. All wires also have inductance which can store some insulation energy as current from the square of the charge carrier flow rate Ec=½LI².
Thus for high frequency AC, all wires will have some impedance due to this ratio of conductor current and insulation current and can be expressed in terms of the reactive lumped values Zo=√(L/C).
The average velocity of a charged particles is NOT current. That's called Drift Velocity.
The velocity of the wave of charged particles is NOT current. That's called the wave propagation velocity, which is equal to the speed of light.
"An electric current [Amps] is a stream of charged carriers , such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume" (using volume resistivity). However, conventionally using lumped elements current is measured by the voltage drop across a known precise very small resistance called a current sensing shunt resistor.
There is a vast number of free charges in conductors that can be excited to move from a voltage source across a closed circuit loop with low resistance. I=V/R Voltage is just the potential to move charges.
Current can flow in insulators according to an exponential rate and their capacitance C. These charges are then stored. Q=CV by a rate of change of voltage Ic = C dV/dt.