First, install packer and VirtualBox.
On Kali Linux, this can be accomplished by running
apt install packer virtualbox virtuabox-ext-pack
Then cp kali-vars.json.template kali-vars.json and fill the values.
packer build -var-file=kali-vars.json config.json
This will upload to the Vagrant cloud.
To avoid doing that and keeping the build local, remove the vagrant-cloud post-processor from the config file.
To run headless builds, you will need to ensure you have the Extension Pack installed and then edit the config.json file to add
"headless": "1",
In the "builders" section before "boot_command"
To build kali-light, it is possible to simply replace the variables inside kali-vars.json.
The kali-light-vars.json.template file is only provided as convenience for building the 2 versions without having to change the var file between the builds.