You are loading it like webPage from server that's why it plays on Your device.
If You would like it to play that sound on RPI, the RPI itself should connect as client to that server.
I would recommend using sockets to play Your sound on node server. For that You will need to use node.js and sockets. There is a module for node https://www.npmjs.com/package/play-sound
You should make Your own server with node and use another device to send socket event to RPI server to play some mp3 files.
If You need to see video on Your other device and play sound on Your RPI like home theater style it will be a problem with usage of server because that sound has nothing to do with RPI, Your other device takes the link for youtube video.
Would recommend connecting display to RPI and browser on RPI making connection to localhost (Apache server).
I can post some example if there is a need to make sound player.
Also use this as start point for making server I made an answer there:
Server