If I understand the first thread correctly, it is not about opening the course from an LMS. When published to HTML the action wouldn’t work properly, exactly as decribed there. But the action does work (normally) when published to Scorm and opened from the LMS in a new window. It depends on the way the window is opened, so it may be related to your setup.
The action does not only close the window, it also finishes the connection with the LMS. But as Sergey mentions in that first thread, all LMS related function are also run when the window is just closed by clicking the “X”. So maybe don’t give the users a button or use custom script to close the window. Just keep the “Exit title / Close window” action somewhere.