That's strange. It should just be the Google Plus profile pic. Does your profile pic appear in other places in Hangouts? For example, if you turn off the camera, does the profile image you uploaded show?
I turned off the camera and saw my profile pic down the bottom of the hangout space, but it still wasn't appearing in the app.
However, after selecting "about google chrome" it upgraded from version 48 to 49, and after restarting chrome it now shows my profile picture ok.
So chalk that down to a Chrome issue perhaps - this was on a Mac running 10.9.5 FWIW.
Sorry to trouble you