The lowermost video on this page shows the real bike from an angle where you can see what happens to the wires:
http://www.stringbike.com/Internal%20symmetry%20of%20both%20...
I think the advantages are because of the location of the torque. When the left pedal exerts force, it torques the left side of the bike which coincides with the the natural movement of the bike. Imagine when a cyclist pedals very hard and the bike sways from side to side from the force exerted on the pedals. Now I'm not sure if they are trying to reduce the movement of the bike, or make it feel more natural.
The thing I cannot make out is the switch from gears to a single system. Is the output of work the same as the force going in, which would mean that you have to pedal the same amount going up a hill as going down, or is there a variability of work like a rowing machine? The rowing machine system would seem to apply here but they do not address that so I'm not 100% on that.
This could be done continuously, rather than having discrete gears.
So, I ask HN: why aren't chain/belt bike designs symmetrical?
EDIT: as to the article -- more analysis of why symmetrical designs are superior would have been nice.
I'm not sure what causes the wire to rewrap itself around the ring on the upstroke... probably some sort of embedded spring.