I couldn't really work out what the problem was. Here are some instructions I quickly created and tested:
Download https://launcher.mojang.com/download/Minecraft.tar.gz and extract it.
In the newly created folder create a script named
minecraft.sh, or whatever you prefer, with the following contents:
chmod +x minecraft-launcher # Just in case
./minecraft-launcher --workDir=`readlink -f HERE` # Use readlink to resolve absolute path
HERE with where you want the portable installation to be located.
When you execute this script, it should run the launcher and game in the specified directory.
For ease of use, you can add it to your menu using "menulibre".
Install menulibre (
sudo apt install menulibre), and open it (search for "Menu Editor" in applications).
Create a new menu entry that executes the script, and if you want a fancy icon, you can add one easily.