I could be wrong, but maybe Fi links to your Google account automatically (which, if you had GMail open, might have opted in to send notifications via Chrome).
Have you tried again? Calling your phone and seeing if you see the call in your computer?
Ok, it looks like it is Hangouts. I had to have a gmail tab open and then it popped up and I could talk through my computer. I dont know if I just never had a gmail tab open when I got a call before or what but I did not know that you could do that.