If I've understood you correctly, the basic problem is that you have both your recorded source audio (your game, in this case) and microphone input recorded together, which is to say, on the same track in Audacity. Ideally, you'd have those on two separate tracks, so that you can adjust their volume (or other properties) separately.
You may want to look into ducking your game audio so that it automatically lowers in volume whenever you're talking. I don't know if you can set this up in Audacity, but you should be able to do this in most DAW programs with a bit of diving into the manual. Most of those packages aren't free, though.
Failing this, one way to bring the quietest and loudest parts together on the same track is by using a compression effect. What this does is proportionally reduce any volume louder than a certain level. That point is called the threshold, and amount of reduction is called the ratio. A 3:1 ratio, for example, means that any audio above the threshold will be one third as loud as it would be without the effect. You can use this to lower your voice's volume. You will, however, experience a bit of a "compressed" sound to it, which is simultaneously more of a "studio" sound, but it brings with it some mild distortion. Adjust it to taste.