The car still has a battery, this goes in the stationary charging system. It's used to increase the current when charging electric batteries. Most electric batteries can accept much more current than commercial electricity drops can provide. This system stores the current in stationary flywheels and then discharges it quickly when a car pulls up and plugs in.
So this provides something like a Tesla super charger, without having to call up the power company to rewire your gas station. They call it a "Kinetic Battery". In the video below, the CEO makes the claim that flywheels are much better for this because you can get many more discharge/charge cycles out of flywheels than with chemical batteries.
You can imagine that rewiring electric infrastructure all over the country would be quite a bit more expensive than just plugging in their system. You could also imagine a solar powered system (off the grid even) slowly being charged and then recharging a car in 10 minutes.
Cool idea!
Interview with CEO https://www.youtube.com/watch?v=YxRfPtYmTDE