Now I have to give a big shout out and thank you to ConfigX, from the Peppermint forum.
This type of file is a container and a special codec is needed to read it.
Open a Terminal window, click Menu >> Accessories >> Terminal
sudo apt-get install lubuntu-restricted-extras
Type in your sudo password and press <ENTER>
Now when trying to play MKV files with VLC, it will work.