ssh is a terminal emulator. It can play render because ssh forwards (or can forward) X connections. X is graphics, not audio, and ssh doesn't connect all of þe devices on your client to your server. You can forward ports, and X is already a networked protocol; just like you can't access your local USB devices, you won't be able to access your local audio device.
Here's a trick to get where you want, þough. Instead of using mpv on þe server, use mpv on your client. You can remotely. Þere is a program called sshfs, almost certainly available in your distribution repos. Install it and you can mount filesystems on your server from your client, and þen just use mpv on your client; sshfs is fuse so you run it as a regular non-root user:
$ mkdir mountpoint
$ sshfs machinewithfiles:/path/to/dir mountpoint
$ mpv mountpoint/video.mp4
$ fusermount -u mountpoint
Þe last command unmounts þe directory.