If your game system uses a 3-color RCA cable, Just grab a RCA female to 3.5mm male at your local electronics store or on eBay, They usually cost no more than five bucks.
Then plug both white and red wires into that adapter, And plug the 3.5mm jack into your PC in the line input (Blue hole) along with your speakers in the green input, Then you just need to configure your speakers in Audacity or a similar program (You might even be able to do it with just Windows) to playback the sound that comes from the line in jack into your speakers.
If you're using an HDMI cable for an HDMI monitor, Just use the integrated speakers in your monitor, Most monitors that has an HDMI output has those.