Inefficiencies always turn up as heat. Since that’s what you want out of a kettle, the only way a newer kettle could be more efficient is by letting less heat escape into the air. But the amount that does so will be negligible compared to the total heat required to bring the water to the boil. And if it takes a minute to boil and you don’t pour out your tea for another minute, more heat will have been lost in that minute of waiting than during the heating period. Another issue is that you’re heating not just the water but the kettle itself so a smaller and lighter kettle may be slightly more efficient from that point of view. But I’m not sure kettles have got much smaller or lighter in the small number of years that is the lifetime of most.
There is one point where a new kettle may win out. Our latest one (bought within the last year I think) has tabs inside showing the 1-, 2- and 3- cup levels, encouraging you to only boil as much water as you need. Many older kettles have graduations on a window but these very rapidly become unusable with even light limescale build-up in hard water areas.
I haven’t had time to watch that video properly but I see it does mention induction hobs. These are good, but the circuitry to generate the high frequency current may well waste 10% or more of the supplied power - note that they contain a fan to keep the electronics cool! Likewise, a microwave delivers heat directly to the food or water you put in it, not even to the container. But my guess is that the magnetron which generates the microwaves and the electronics which power it are less efficient than an induction hob.
But in short, Boris will be more use to humanity finishing off his biography of Shakespear than spouting about things he doesn’t understand!