Once you've downloaded the .zip file from the website, you'll want to extract the file to your Space Empires V Empires folder. All empires for Space Empires V are placed here:

    ..SE5\Empires

If you are using the steam version of Space Empires V, your install may be buried deep in a folder like this:

    C:\Program Files (x86)\Steam\steamapps\common\SpaceEmpiresV\SE5\Empires

If you extracted the race correctly, it will have its own folder in the Empires folder:

    ..SE5\Empires\[Empirename]

For adding custom races to the Balance Mod, check out HERE.