It has to be done via your hosting panel. Look for Fantastico in your Cpanel and you can install wordpress on any domain you want. If you can't find it make a google search.
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I moved from godaddy to hostgator for this reason. I didn't want to take the time to learn how to install and create a database. I'm sure it's easy if you have the time and practice. Hostgator makes it easy to install several cms systems. You should check it out. Good luck!
It can be done from your hosting panel, if you do not have Scrip install software, it can also be done manually. If you need any help, feel free to ask.
Manual process is best, Download wordpress source code form wordpress website, upload code on your server and create database and open your website, it will ask you to set up and all it will ask you to database and server details, once you will enter this your wordpress website will setup.
So you're stuck with whatever older (and easier to hack) version Hostgator has available, instead of spending 5 minutes learning how to install WP manually. When you're hacked you'll spend a lot more than 5 hours trying to get your site back (and failing to).