If you want to back up a website hosted at HostGator and upload it to your hosting account at Hostinger, follow these steps:
Log in to your HostGator's cPanel.
Click on the Backups menu in the Files section.
Under the Full Backup section, select Generate/ Download a Full Website Backup.
Select the Home Directory option from the Backup Destination drop-down menu.
Specify your Email Address if you want to get a notification when the backup is complete.
Click on Generate Backup, which will create the backup file in tar.gz format in your home directory.
Now, you can then download the backup via cPanel, FTP or SSH.
Additional Resources
See our full guide to transferring from HostGator to Hostinger: How to Cancel A HostGator Account and Transfer Your Services
You can check the guide from HostGator here: How to Generate & Download a Website Backup
If you need further help, make sure to contact HostGator support