In that script, line 5 you have something like this:
OPSYS=$(cat /etc/lsb-release | grep CODENAME= | sed -e 's/DISTRIB_CODENAME=//')
When you use Mint, it detects OPSYS variable as maya which is what mint 13 is called. Obviously there is no such repo for mint and the script returns an error. Luckily mint is based on ubuntu, so you only need to modify that script a little. Replace that line I mentioned with this one:
Save the file and execute it with
sudo sh install-esteid-ubuntu.sh
If everything went well you should be able to use our ID-card software.