The theory on this is correct, but the ICL7660 is not designed to provide the kind of current you'd need to run a 12W audio amplifier. It maxes out around 50mA - see figure 7 of the datasheet[1]. 50mA*17v = only 0.85W.
Because I can't see the datasheet of the audio amplifier, it may be wired in a way that it doesn't use significant current from this supply (for example, in the pre-amp part of the circuit). But then we wouldn't be getting the advantage of 17v supply to make it louder than other games.
When overloaded, simple switching power supplies like this lose their regulation. In this case, the switcher operates at 10kHZ, so it might introduce a high-pitched sound to the output.
You can probably get away with connecting the -5v input to GND to make the circuit run at 12v instead of 17v. Or, look for a more capable negative power supply.
[1] https://www.renesas.com/us/en/document/dst/icl7660-datasheet