I'm not completely happy with the way he describes Fe in the video. For me, it isn't simply observing other's emotions but how I evolve a picture of what makes others, by themselves and collectively, tick as a whole, and that determines how I interact with them. I can't really split it off from my other functions and see it only as a way of feeling and influencing emotions of others. It isn't simply an awareness of emotion, which is perception, but a way of judging what is going on, on the fly out there and taking action on it in the external world. For me it's very much bound up with outward facing values as well as the emotional flavour of situations. The importance of values is that they both act as an anchor and also can transcend immediate harmony - if I were a teacher, I might put an unruly class in detention and that is certainly not harmonious in the moment, but is based on the collective value of learning how to behave well socially.
You are dead right that predicting others' emotions in some kind of superpower way is not the way we work. For me it works in a couple of different ways. One is that I get to know someone over a period of time, build up a good feel for who they are, and then I get a much better feel for how they will react emotionally. The other is in the moment, and is pretty well unconscious - I react to the other as we interact and adjust my behaviour dynamically. I'm not so much predicting the other's emotions as doing a sort of windsurfing or skiing in the present moment, evolving my reactions on the fly, based on the body language 'terrain' of their reactions which are often very different from what they say. I must say, the second of these takes a lot of energy from me, and I don't bother unless the situation warrants it.