RJ45 convert to serial with FT232RL
First of all this cable looks to be a proprietary cable for connecting a computer to a Cisco device of some kind that uses an RJ-45 connector. The RJ-45 connector is what makes this a non-standard/proprietary cable.

However if you carve the gob of plastic at the USB end open you'll find a small circuit that is powered from the USB interface. Based on the description at the link you provided this circuit is composed of an FTDi USB/RD-232 converter and a ZT213 RS-232 level converter. The FTDI chip handles the USB protocol simulating a USB Serial device on the USB side. The ZT chip converts the output from/input to the FTDI chip to/from RS-232 level signals.

The only RS-232 pins required to move data are Tx, Rx and GND (transmit data, receive data, ground). The other pins are all "modem control" pins or special interface pins. This includes RTS (request to send), CTS (clear to send), DTR (data terminal ready) and DSR (data set ready). When connecting two devices together without actually using a modem these are typically cross connected to either control the flow of data (CTS/RTS) or the existence of a device (DTR/DSR). Occasionally you'll find the converter circuits powered from these control signals.