The Google Home has no way to directly control other devices on the same network or through other wireless protocols. Everything goes through an Internet-based service and expects to communicate with devices via a server-based proxy. How that server communicates with the device is up to the developer.
Depending on your needs and capabilities, you do have a few options.
One option, for example, is to use a tool like ngrok to create a tunnel between the device itself and a service run by ngrok on the public Internet. Calls to the public https address are sent to a service running locally on your device, and you can handle it accordingly.
Another is to have your device connect to a server and listen for command changes, and then execute those changes. If you don't want to run a server, you can even use something like Firebase - have your device listen for changes on the real-time database (which can use the HTTPS port to communicate as a client, so you don't open anything) and have something like a Firebase Cloud Function act as the webhook for your Action.
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