There is no official Google Hangouts app and may never be due to Google's nearly non-existant support for Windows Phone.
There is an API for developer to use so it's possible, but as you've noticed, no real fully featured 3rd party apps for Hangouts exist (yet?).
There is also no way to use a web version of Hangouts in Internet Explorer on Windows Phone.
There is a bug in Windows Phone 8 and Gmail. A suggested solution is to use POP:
On Windows Phone 8 when you set up a Google Mail account you are
offered two options: ‘Email only’ or ‘Email, contacts and calendar’.
That latter option is the push-IMAP2 version while ‘Email only’ is POP
and will give you just 15-minute sync periods.
There are also ...
Per your link, the correct answer is:
The ONLY way to change the primary Microsoft account that is used on the phone is by hard resetting the phone & setting it up agaib with a different Microsoft account. When you reset the phone the phone will be returned to the state it was in when you bought it. All your personal data and any apos tou installed to ...
There is no official Google Hangouts app for Windows Phone.
You can use IM+ or Agent + ICQ apps. They are not official or fully functioned but still better than nothing.
See http://www.guidingtech.com/29720/gmail-maps-gtalk-windows-phone/ for review.
See reddit thread for discussion.