It's not the load on the RC, but on the chipset in the drone. When your record video, the CPU is getting more of a workout. Modern CPUs don't run at a constant clock rate, they at a speed fast enough to do what they are asked. The faster they clock up, the more power they draw. The
Mini 3 uses H.264 to write a compressed video stream. That's a lot of processing, which will spin up the CPU clock speed, which in turn is a higher draw on the battery. I don't know how much of a hit that would be, but I would guess it would be more noticeable on a smaller drone.