As you can see on the circuit schematic, each middle LED is controlled by two outputs. If these are both low (so they put out the negative signal) the central pin of the transistor is supplied with a resistance of 23,5K(due to the diodes the current does not flow through the low resistances).
When one output takes the high level the central pin of the transistor is bypassed by the low resistance connected to that output.
So the transistor collector turns off and the LED becomes dark.
In the video the circuit works at the maximum speed, but you can make it faster by using a smaller capacitor.