This would need to be checked with Chaturbate themselves, but the main reason that Chaturbate don’t allow the playing of games (console / computer), watching Television or Movies on cam or allowing viewers to see this in the background is all down to copyright.

Chaturbate DO stop the playing of music that is under Copyright via recorded videos that are sold via Models Galleries.  As they automatically mute videos that contain music even if there is no copyright on the videos.

An email will be sent to confirm what the rules are regarding music on live streams and this answer will be updated once a reply has been received.

UPDATE:

Answer from Shirley has confirmed that playing copyrighted music is also not allowed.  You can only play music thats ‘royalty free’.