Except defining the off state the resistor R1 in the base is important when you require faster on/off speed. It discharges the parasitic and Miller capacitance to the ground.. Not so important with a relay, though..
If one looks carefully one notices a connector in the base circuit of the transistor in question. The resistor R1 in the base circuit isn't redundant, it is good engineering. If the connector is disconnected without the resistor the base bias is undefined. with it the base bias is defined for all conditions. Bob