Hangouts hides itself in system tray
After extensive playing around with different settings, I was never able to get anything to work. It seems that any application that is updated is automatically relegated to the hidden part of the system tray, regardless of the old settings for the application.
However, Google released a Chrome app for Hangouts (as opposed to the old extension) that removes it from the system tray entirely. Using the app, Hangouts now has a proper Taskbar icon, and behaves more like a native extension. I know it doesn't exactly fix the original issue, but it removed the issue entirely for me.
Apparently there can be 2 issues.
The first one is a priviledge error. Shameless copy pasting:
Program Files (x86)\Google\Chrome\Application > right click chrome.exe > Properties > Compatibility > Change settings for all users > and tick "Run this program as an administrator"
Or this can be a profile error, can you try it with a different profile?
Hope this helps.