I'm not sure how this could've occured. Normally the pure song outside of the game sounds alright to me. Maybe some other thing occured on the game what influenced the overall sound experience. Another possibility could be, that the stereo panorama of the different instruments are to distant to each other, so this bitonal effect occures. I'm not sure, if I can fix such a problem. Nevertheless I really appreciate your additional answer on my question. It might help me to improve the quality of my creative work. :)
By the way I reworked some aspects of the song, because of some feedback of the dev. Maybe the new version will be better, although I'm unsure, when the new song will be implemented inside the game itself.
Edit: The dev showed me the video of the bitonal effect and it seems to be a game bug. It is really strange indeed.