I actually watched the entire video and learned a few new things along the way so that was pretty enjoyable as well.
Just because we put everything about us into an AI somewhere and sometime in the future, it will at best, just be a Clone of us. It might be able to recall some events, dates, and jokes or storylines from our past to tell to others in a storybook fashion. Still, it will never be us and we (the original person) will never become immortal or live for eternity.
One has to be conscious for that to happen and at least for now, AIs are not conscious nor do they have a comparable working brain. No real soul, no human personality, and no human emotion and understanding.
Perhaps in the next hundred years or so, if the world is still a viable habitat, we shall see.