I know that speakers produce sound by creating a pressure wave, but I don't understand how when they play music or games you can hear the different sources. I guess what I'm asking is how do they play (or seem to play) multiple frequencies and amplitudes simultaneously?
An arbitrary periodic signal can be decomposed into a sum of pure tones of varying amplitudes and phase. This is called Fourier decomposition.
So, for example, a sawtooth waveform, much like that produced by a violin, has many frequency components of distinct amplitudes and phase. The loudspeaker simply reproduces the sawtooth waveform.
It isn't remarkable that a speaker can, within certain bounds, produce an arbitrary periodic acoustic wave.
What's remarkable is that our ears and brain can, in many cases, interpret that complex acoustic signal, whether live or reproduced, as separate tones, instruments, etc.