ok lets make sure you can play the files LOCALLY on your source computer first. no need to right click on the music files, just open up a computer mp3 player and choose a file to play.
on your device, use another music player. poweramp is highly recommended.
the htc transfer tool uses dropbox and its has been unreliable for some people who have posted on this site.
in my opinion, and for locally stored files such as music, videos, and text documents, i just transfer them locally to a computer or HDD or a thumb drive directly attached to the htc one and offload files that way and use google servers as the recommended backup for other data.