I am want a group conversation chat by voice and I know this can work in an application made maybe in node.js, react.js example: free4talk.com but I begin to doubt if it is possible with wordpress. And I also do not understand how the google hangouts API works if it was closed for developers. developers.google.com/+/hangouts/support-faq
You will no longer be able to use the Google+ Hangouts API! I would suggest using some already built plugins, for your Wordpress website. Here's a list: https://wordpress.org/plugins/tags/group-chat/ There are many third-party chat service providers, which you can use. The benefit is that you won't have to buy an expensive hosting package, as these services runs in their servers and you no longer have to worry about updations, bug fixes, etc. As the service provider will do that for you. You only have to pay a small fee monthly. Hope this helps!