Hangouts on Chrome uses a variety of Chrome-specific APIs to make video and audio calls work (or at least it used to). For other browsers, Google developed a web plugin, but that became a problem when Firefox dropped support for plugins (besides Flash) back in March. It has taken a long time, but Hangouts finally works in Firefox again.
— Tsahi Levent-Levi (@tsahil) December 20, 2017
At least on Firefox, Hangouts now uses WebRTC for video and audio calls, meaning no plugins are required.
Hangouts calling now works on Firefox without plugins was written by the awesome team at Android Police.