You won't be infringing the copyright in the recording (P in a Circle) but you are infringing the copyright in the composition, which you seem to understand (C in a circle ©).

Its up to you, if its free and it doesn't go viral, you are probably not going to get sued for it, They original owner may ask you to take them down if he finds them offensive or discrediting to his original work. I would recommend submitting an inquiry to the publishers of the developers of the game, explain that its gunna be free.

(Disclaimer: I am not offering legal advice, I will not accept any responsibilities for anything that will happen to you for infringing these copyrights.)