I'm not a lawyer, you are not my client, this is not legal advice, I will not represent you in court and so on.
I'm assuming that the music/songs will be stored and transferred by your servers. The reason for this assumption is that we are talking about an MMO.
What Almo comments is correct: The EULA for the game in question should have language about this issue.
What if one were to create the MMO in question?
Then the EULA should still have language about this issue. The difference is that you need to create the EULA. Thus, I would suggest to get the help of a lawyer to write it.
The way I see it the main decision is the following:
The players agree to transfer ownership of the works to you.
If the players transfer ownership to you, you will be able to do whatever you want with their work (sans obscuring the identity of the original author, unless they prefer to remain anonymous).
However, it also means that any works in the game that violate some other copyright are your responsibility. In other words: you would be liable. And thus you must actively police for copyright violations to make sure that does not happen.
The players retain ownership of the works, and license them to you.
If players retain their ownership, you need to include in the EULA that by playing the game they agree to license their works to be used in the game. You will also need language to the effect that you are not responsible for the works created by the players. And then you probably only have to deal with copyright when reported (e.g. notification of infringement).
If you ask for my opinion, letting the players retain the ownership of the works is good for the players (because they have the copyright of their works, they can use them outside of the game) and for you (you are less liable, and it is cheaper to not have to actively police for copyright violations). In fact, if I were a potential player and this game wants me to transfer ownership of any works I create inside of it, I - personally - would not play it, because I would consider this as the game taking my labor.
Then you need to decide what to do when you find a copyright violation. Be aware that whatever you do, it will not erase the past, and copyright holders might still want to collect from you or your players.
Now, that you are aware that there is infringing content in your system, you can remove the work, or you can try to get a license for it. You can guess which is the cheaper option of these two. Getting the rights would be at a loss unless you can monetize the music. Consider also that such monetization might be attractive.
Other decision include:
You need to decide how will the music/wongs be shaded in the game. Will players send messages that allow access to specific works, or will there be a public list from which they can choose what to listen to, or will the game decide what they will listen to from what is available, or something more complex like you can approach another player and listen to what they are listening, or ven listen as they create the music?
And you need to decide If you are going to monetize or not, and how. For example will players pay by listening time or purchase songs.
I mention these decisions because it is not clear to me when you would need performance rights or broadcasting rights. Thus, I'm suggesting you bring this topic to a lawyer.
Furthermore, there might be some caveats I'm missing. For instance you mention original samples, which would have their copyright. Also be aware that the law is not uniform across the world. Ask a lawyer.
Would the players be able to share and play (in-game) the music they create freely?
Will the music/songs be stored or transferred by your servers? If so, you need the right to distribute it (you might need other rights, ask a lawyer). And this are rights you need to get from the players (or get ownership of the work). In other words there must be a legal agreement that grants you these rights, that you present it to the players, and have them agree. Otherwise your servers would be copying and presumably sending the work to another player without the permission of the author, and that is a copyright violation.
Would there be a difference if it's an original song vs a cover of a copyrighted song?
So... Is the player really the author of the music/song? In other words, can the player really give you rights over the work?
I believe that if you take the player authorship on good faith a lawyer can help you right a disclaimer for this situation. However, be aware that if you actively police for copyright violations, that means that you are not taking the player on good faith.