You'll have to edit the audio. FFT the waveform, and adjust the low frequencies.
That's a band-aid fix, and you can easily ruin the quality of the audio by using an equalizer without understanding how to use one and how harmonics work. Plus he mentioned that the recording itself sounds distorted. No amount of post processing can fix that.
OP, your audio card records audio digitally. Using the right settings, any digital audio source, such as the audio output from a game, can be captured by any audio card without alterations, assuming the audio card is set to use the same or higher sample rate than what you're trying to record. It sounds like your audio card has some sort of bass boost activated, which is being recorded along with your gameplay. When you watch the recording, you're hearing the bass boost twice. If possible, please post a recording of you playing, along with a recording of any track from the music room of the game you're trying to record (it's ok if they're 2 separate recordings). I can analyze the audio and I may be able to give you a better idea of what's going on.
Some more info about your hardware and settings would be nice too. Are you using a prebuilt computer? What's your motherboard? What's your sample rate set to? Are you sure you have the latest drivers for your audio card installed, and if so where did you find them? What's your music and SFX volume set to in-game? Is fraps set to record any audio input? Try disabling that.
If you're looking to replace that audio card, don't google for "audio card", you'll only get junk looking for that. Look for USB audio interface. Compared to on-board audio, audio interfaces give you more control over the audio, along with having higher audio quality (specially noticeable if you already have decent headphones or speakers) and lower audio latency. As for alternative recording programs, you can try OBS. It's way better than fraps for most people.