From what I've found, Eminem (or Mathers) is credited on this song as Writer and Producer.
From Discogs and Wikipedia:
Eminem is an American rapper, record producer.
Also, about his own producing style:
Eminem is considered unusual in structuring his songs around the lyrics, rather than writing to beats. (...) After doing little production on Relapse and Recovery, Eminem produced a significant portion of The Marshall Mathers LP 2.
He said about producing his own music,
"Sometimes, I may get something in my head, like an idea or the mood of something that I would want, and I'm not always gonna get that by going through different tracks that other people have made. They don't know what's in my head. I think maybe it helps, a little bit, with diversity, the sound of it, but also, I would get something in my head and want to be able to lay down that idea from scratch."
Here is a list of his work as a producer.
You can also note that a record producer may have different roles in the project other that music instruments, hardware or software work:
- gathering musical ideas
- collaborate with the artists to select cover tunes or original songs by the artist/group
- work with artists and help them to improve their songs
- supervising the entire process
- gathering the staff (audio engineers, studio musicians...)
So one can be a successful producer without knowing any knowledge in music theory or in how to play any instrument.