Note that you need two separate and independent relays, not just one. CrossRoads' diagram uses the left relay as an "enable" control and the right relay as a "direction" control.
Issues with your wiring are:
- transistor emitter is not connected to ground
- base resistor is not connected to arduino at all
- relay coil high side needs to go to VCC/5V not D13
- your red wire is not connected
- the relay Common pin is not connected
- only half the circuit is present
As a temporary measure with 1 relay, you could connect the red wire to the relay common. That way the actuator will ALWAYS be moving and this relay will control its direction. I don't know what will happen if you try to drive the actuator through its end-stops.
I have a handful of this exact model of relay. The way it's in the breadboard makes me think you've folded the common pin under and maybe you don't have the other wires plugged into the right columns.