Using some WAV recorder, you could patch your audio output into your mic. jack (or whatever input the WAV recorder is listening to). Start the recording process, play the game, close the game when finished, and stop/save the recording.
You dont need to patch the audio outside the machine, you can do it all internaly without any loss of quality, all you need to do is the same as what SimJ said, but set the selected recording thing on your audio slider controls to either "WAV/MP3" or if you dont have that, something along the lines of "All" "Stereo Mix" or something else different compaines give them different names.
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Thats how I'd do it anyways.
NS