I created a similar script using BASH and posted it here
. About the only real difference is that I included the version as a parameter (useful for when I update makemkv, rather than touching the script I just do makemkv-install 1.6.5) and I stop the script if any of the builds go wrong. I did include text for a workaround apparently required under Lucid and a few other systems, but since I'm too lazy to spin up a Lucid VM and test it myself I wasn't comfortable actually implementing the change automatically (a pretty simple sed command).
I do like how you've created a GNOME menu entry, I may have to update my own script to do something similar. If you're running a reasonable version of Ubuntu or otherwise can get PPAs to work, the document I linked shows how to install from a PPA so it will get updated automatically (if you'd like to create a PPA yourself you can check this
A more trivial comment, I chose my name intentionally because I'm forgetful. I have a recipe manager (Gourmet) and I wrote a script to process the recipe filenames after I export them to HTML. I called it something like process-recipe, but when I use it once every few months I could never remember what I called it so I had to check ~/bin. I renamed it recipe-process and now I know to type "recipe" and let tab completion figure out if it's really recipe-process, recipe-rename, etc. Similarly since I designed my script to be used on MakeMKV updates, I used makemkv-install so I can tab complete it after typing makemkv (in case I forget if it's -install or -update or -download, etc.).