Hi there,
I am on Windows 10 also and was having the same issue, so I thought it was a Window 10 thing. I found Karaoke for DirectX 2.3 on another site, was recommended so I tried that and edited the registry file as they recommended and it still did not work.
But I ended up just right clicking the CDG file and selecting Open With, and then selecting Windows Media Player, and also selecting the "Always open with this program" check box. This actually got it to work for me. Do your CDG files show the Karaoke for DirectX icon or Windows Media Player icon? They should show the Windows Media Player icon. When you first open it this way, you also get an error message from Windows Media Player, but you can select the "Never Show this again" message box thing.
Sorry if this is a newb response and you already tried this, but I was getting frustrated with it not working for me and I felt silly that the fix was so easy, at least in my situation.