FYI, the “Old one” is still valid, but is intended for people who want to use their own instance of Myopenhab cloud (not the official myopenhab.org).
It’s mainly for developers who want to test or implement new features before they are officially published, or for people who want an installation which doesn’t rely on the myopenhab.org servers.
If you’re the “standard” user profile, ie have a local openhab installation linked to a cloud account with myopenhab.org, then use this tutorial @bartus pointed out to you : Google Home & openHAB connection How-To
If you are more a techy guy who wants to contribute and test/implement new features in openhab that are not yet released, then you can follow this guide here (your original link) : https://github.com/openhab/openhab-google-assistant