Notice from the schematic how the DS2405 addressable switch outputs are connected to 2N3904 NPN transistors. This is because the DS2405 outputs can only provide about 4mA sink [ground] output current. The 2N3904 NPN transistors allow the DS2405 limited capacity outputs to easily control higher current devices.
Since the open-drain outputs of the DS2405 addressable switches cannot produce a logic 1 output, the 10K pull-up resistors are included to pull the NPN transistor base to logic 1, and turn on the LEDs. When the DS2405 output is on, it will apply ground to the base of the NPN transistors, turning the LEDs off.