When you connect the relay parallel to the power button of your case you will not need the standby cable.

You would only need it when you want to use the ATX break adapter and when USB (which normally powers your aquaero when the PC is turned off) is not connected. In this case you would not be able to turn on the PC anymore when it has been turned off by the relay because when it breaks the power, also the main power of the aquaero gets interrupted and the relay is not able to switch back in its normal position. By using the standby power the relay is able to switch back so you can turn on your PC again.