You didn't dig deep enough!
On that same page each version download listed shows minimal requirements. The 2.9.x version has these:
Might want to map out and check each hop you plan ... upgrade notes and 'requirements' ... compare them to what you have access to/can do with your shared hosting at hostgator.
If this server is on hostgator shared hosting am assuming it's linux based therefore download the .tgz - smaller package for Linux. The zip is larger and perhaps best suited for Windows. I also assume whatever control panel you have with shared hosting can un-compress a .tgz.
Maybe one of these? ....
Me thinks, however, with shared hosting, you will hit a wall concerning database before version 3.6.x.