If the XBox supports DLNA/UPnP just enable the Media Server in MediaMonkey (and set it up according to your needs) under Tools > Options > Media Sharing.

I have Media Monkey v4.1.0.1692 on Windows 7 and was wondering how I can stream my music to my new Xbox One. I've scene online that you could stream the music using Windows Media Player, but I was wondering if there is a way using MediaMonkey I can do it. Any suggestions?