Ground means different things to different people.
In electronics, ground is a common point on the power supply that measurements are taken from. For instance, in a typical computer power supply, you have 3 different voltages. The negative side of the meter is attached to ground, +5 volts is measured on one supply, -5 volts is measured on another, and +12 volts is measured from the third, IIRC. It is a base point for all measurements, whether DC supplies, or AC signals like in Wayout's schematic.
To an electrician, ground (aka "earth" as it is know to our friends across the pond) is the third wire in the power outlet. It is tied to the chassis of the machine in question, and is intended to drain away any harmful voltage should raw power come in contact with the chassis. The hope is to trip the circuit breaker and avoid shocking the purple hell out of whoever comes in contact with it.
As far as I know, there is nothing that says that the power supply ground has to be tied to the chassis ground, but I think most times it is. And I've seen systems where signal ground was kept seperate from power ground, but I doubt that would ever apply here.
On a side note, do not assume one side of the speaker is always tied to ground. I don't know if they have any bridged amplifiers (LONG story) in pinball machines, but neither side of the speaker is ground. To ground one side would let out the magic smoke.
HTH's