Select "Allow" for both Google Talk plugins in order to access the video call.
Of course, there isn't anything to click to enable the plugins. Weird.
Eventually, I found out that by telling Chrome to automatically run all plugins, it would work.
chrome://settings/content
Scroll down to "Plug-ins" and select "Run automatically (recommended)"
Once that's done, start a video call; works fine.
Since I'm paranoid, I went back and changed the Plug-ins setting back to "Click to play" and, guess what? Video calling still works!