WHOOYOO. I have fixed this.
Problem: My music files were .wma.
Test: I had one file which was MP3 and when I tried it, it worked.
Resolution: I converted my .wma files to .mp3. IE11 now plays my playlist.
You can download a free converter from cnet.com. Here is a link for converting WMA/WMV/ASF TO mp3:
https://download.cnet.com/Free-WMA-to-MP3-Converter/3001-2140_4-10494267.html?hlndr=1
Note* It will install a bunch of garbage before installing the software, so you will have to uninstall these things after converting your files.
Resolving this issue.