Streamers as well as web cam models _aren't_ allowed to play random music, they just do.
The only time it's allowed is when they have the appropriate licenses. (sync license under DMCA for music synchronized to live streams)
Streamers were doing this without repercussion 5 years ago because the streaming industry wasn't large enough for the music industry to care about. That changed about two years ago.
The same holds for cam models, it's just that they're not getting claims for whatever reason. Maybe the music industry just isn't that focused on live pornography?