If the material is stereo you could try vocal removal in Audition, if the track is mono there is nothing you can try.
As far as I know this cannot be done. Unless you do some really, REALLY intense editing in Adobe Audition.
I am a fellow lets-player and what I do is record my microphone input with a free-ware program called Audacity and record the game sounds with Mirillis Action! (or FRAPS, whatever you use). This way my voice and the game sounds are seperate.
In other programs like Vegas Pro, voice was in a different channel than game sounds. But the same gameplay in Premiere Pro is in the same