How can I use an Android phone as a media player?
This is entirely possible via mDNS/uPNP/DLNA. You don't even have to use a phone for that. Cheaper variants exist, such as dedicated android-based microcomputers with size of a bigger USB stick.

All you need to do is to install an app that will act as a media player with DLNA support. There are plenty of these available, one such app can be DroidUPnP or Yaacc, both available via F-Droid. You can then setup the app as a player and control it from a remote controller software, such as ControlDLNA, also available from F-Droid.

Setup is automatic, you just need to fire up a few servers as media sources. These can be computers, xboxes, other phones and pretty much anything that has a DLNA logo on it.