Don't give up too soon.
I can't say for sure about the IC shown in the original post, but I have seem similar boards in toys which drive a small 8 Ohm speaker. A speaker is normally used when a piezo transducer doesn't have sufficient frequency response. It's normally a crappy plastic speaker about 25mm or 30mm in diameter, but a larger 8 Ohm speaker will work and sound much better. An efficient reflex horn, designed for PA and security alarm applications might even be quite loud.
Have you looked at the output on an oscilloscope? I suspect it's a class-D PWM output stage. If you want to drive a larger speaker, you could try a couple of MOSFET drivers, connected to suitable MOSFETs, running at a higher voltage of course, with the chip powered from 3V. You might need to add a small filter to cut down on RFI and reduce the power consumtion.