For such simple sounds I'd rather use some kind of buzzer rather than a speaker.
With a speaker like this you will definitely need some extra drivers to get enough volume while not grilling your GPIO.
On the other hand, your amplifier is meant for I2S communication but while the Photon has I2S capabilities there seems to be no simple library to facilitate that.
For your intended use that'd be way over the top IMHO 
If you'd want to play some simple wave sounds you could use an analog amplifier like this
and the DAC pin(s) on the Photon with this library
For even more elaborate sounds you could use this cheap MP3 module (with onboard amp)