Is it possible to deploy a Django website using HostGator shared Linux Web Hosting?
Is it possible ? Yes 
Is it recommendable? No
as it says on the same hostgator page:

While it is possible to install Django on HostGator servers, it is not a supported application

This means that hostgator is not designed to host django. My recommendation would be:
If it is a simple project: Use Heroku
If it's a project that might later become something bigger: Use google app engine (google cloud) or Elastic beanstalk(AWS)
I am looking for a solution, to deploy my Django app on my Unlimited Linux Shared Hosting Plan on Hostgator.