The buzzer appears to a be a piezo (nothing more) which behaves as a capacitor. To make it operate you have to drive current into it and then draw the charge back out, that is you have to sink and source current - a single transistor will only do one.
Edit: Ooo! a circuit has appeared! But it doesn't change my previous explanation. When you close the switch the "speaker" will charge up. Then, when you open the switch, .... nothing happens, the piezo remains charged. The datasheet specifies that the speaker is designed to be driven with a 9V p-p square wave, i.e. you have to drive it with a square ware, it's not a buzzer. You could try a resistor across the speaker terminals to remove the charge.