Rubber wouldn't hold up to the metal contact while shifting unless you reengineered how it shifts
This bike has a rear hub that has the gears built in, the assembly does all it's movement internally (planetary/epicyclic gears) and only uses a single rear sprocket with no derailleur or tensioners required... so the chain, or belt in this case, behaves exactly as it would in a single speed application.
They are commonly seen on hybrids and commuter bikes. Internal gear hubs have been around for ages but have gotten much better in the last 10 years or so.
The only way you can have gears with belt drive is with an internally geared hub. Since there is already a solution for the gear problem, there's no need to re-invent the belt to suit traditional cluster arrangements.
For super low maintenance commuting the belt drive/internal gear hub combo is awesome.
The only real downside to belt drive is that you are limited to single speed or a belt drive/internal gear combo which limits it's usefulness to where those setups are practical. Each to their own.