Need some assistance with cleaning soundtrack

I don't think there will be any way to do that automatically. You could pretty easily replace them with silence, or static, or repeating some part of the music using an audio editor like Audacity, if you might find that kind of noise less annoying than the game sound effects.

Maybe, maybe, if the music and sound effects fall in really obviously different frequency ranges you can use EQ to lessen or completely hide the sound effects, but you'll need to operate on each noise on a case-by-case basis. In the case of a game recording I'd be really surprised if this would work. It's more likely to work for separating human speech from music/environmental noises because the human voice falls into a pretty narrow range.

Perhaps someone who is really skilled with audio effects can edit it well to hide those sounds, but it'll probably be a big job and be more like artistry than a technical feat, in my opinion. :)

Good luck!