Well I certainly have doubts about the original schematic. The schematic now - is still really a block diagram and not complete enough to work with. This presentation is about using a Ultra-Cap for bulk energy storage in conjunction with batteries - since we are talking energy storage, typically the more the better, but you pay of it with size and weight. The later schematics - showing the switches for control, are closer but still not close to the whole system. If you look at the photos of their systems there is clearly a lot more going on than in the schematic you first posted.
Sizing the caps comes down to how much energy do you expect to store, in this case from regen braking, so the sizing is almost more of a mechanical calculation: Max Speed, Max Weight, inertia, total kinetic energy that needs to be regenerated back into the cap. They are using a different topology - series vs Parallel connections, and the controller needs to actively regulate the braking effect and current flow INTO the Ultra-Cap.
Also this motor is actively field controlled - another level of complexity - I would probably avoid on a cart.