To rebuild the computer's main drive, you must start up the computer from another source. There are many options to do so.

The downloaded software will not start up your computer since it does not include any System files. 

You will need to utilize one of the following configurations to use the legacy DiskWarrior 4.x application (please read carefully as not all of these may be relevant for your configuration):

(1) Alternate Startup Disk

If you have an external drive such as...

FireWire (PowerPC or Intel) USB2 or newer (Intel only) Thunderbolt (Intel only)

(2) Or a secondary internal drive or partition...

You can download and install OS X 10.10 Yosemite (most recent version supported by DiskWarrior 4.4) nn that drive; start up the computer from the operating system on the external/secondary device. Once you have started up the computer from the newly-installed operating system, install DiskWarrior into the “Applications” folder. Then, you can launch DiskWarrior from the Utilities folder of the external/secondary device to rebuild the directory of the computer's main hard drive.

Please review the following link to see how to utilize the downloaded OS X 10.10 Yosemite to install the operating system onto an alternate drive:

https://support.apple.com/en-us/HT210717

(3) Target Disk Mode: Connect two Macs with a FireWire or Thunderbolt cable (not all options will be applicable depending on the model of your computer) where one is the “host” and the other is a “target”. The host Mac should be running OS X (10.5.8 "Leopard" or higher). In this scenario, the target Mac is the computer whose internal hard drive you want to repair. Start by shutting down the target Mac. Then turn it on while holding down the “T” key. The target Mac’s drive will appear as an option via the DiskWarrior interface. Run DiskWarrior from the Applications folder of the host Mac and rebuild the target Mac’s disk.