The main use of capacitors in circuits (if we go by capacity) are bypass capacitors. These are essentially small buffers of electricity that can charge and discharge quickly when a jolt of power is needed downstream.
Without bypass capacitors every sudden draw of power would pull the supply voltage of the whole system down, especially if your power source (battery) can't react that quickly or has limited discharge rates.
Without having looked into the plans here, I'd expect a super-capacitor solution to look like this:
1. You charge your cars of super-capacitors super quickly at special charging spots and drive away
2. The stored charge is then partly used for driving, partly used to charge the cars actual battery and partly used to act as a bypass capacitor to smooth out the load for the battery
3. Eventually the capacitors are empty, but you had a short charging process that filled part of your batteries