Single speed and a chain that isn’t a chain …

No doubt I’m exposing my ignorance here, but someone in Wimbledon is parking a grey Trek single speed with what looks like a rubber chain on it: i.e. there are no links, and the teeth seem to be of the same material as the chain / belt.

I was just wondering if anyone’s seen this before, and whether it offers significant advantages / disadvantages?

(For the record, I’ve decided I’ll have to buy a geared road bike next time – I can’t hack Wimbledon Hill without gears!)