It looks like you are pointing to the wrong folder. Usually the public_html folder is in the www directory. I would set up a virtual host and store openEMR there. Here are easy directions to fix that.
Set up a virtual host by following the directions above.
Copy the files from OpenEMR into the folder that you want.
You should then be able to install OpenEMR
A few things. I don’t know how familiar you are with Linux, but the ‘~’ does mean home/username. Remember that the public_html folder is usually found in the /var/www/ directory.
When you first turn on your computer and you open a terminal (CTRL + T) typing the command ‘pwd’ will give you your current location. Chances are you will see
/home/username
If you are navagating in different areas of the file hierarchy in Linux and if you want to access the /home/username directory, you can use the ‘~’ to access it. For example: ~/Documents/mydoc.doc is equal to /home/username/Documents/mydoc.doc.