According to this thread, despite charging people lots of money for their operating system, Microsoft decided not to pay the for the licensing rights that would allow Windows Media Player to play DVDs in Windows 8.1:
http://www.tomshardware.co.uk/answers/id-2229969/windows-play-dvds.html
However that's no great loss because Windows Media Player is a pathetic video player anyway. The free player widely recommended in the technical press (and on BBC technology programmes) is the one mentioned in that thread, i.e. VLC:
http://www.videolan.org/vlc/index.en_GB.html
VLC is definitely outstanding but it's also got a lesser-known rival, which is at least as good, called GOM:
http://www.gomlab.com/eng/
Either of those should fix your problem.