The thing about playing most instruments is that you have to be simultaneously "in the moment" while also thinking about where you need to be in the next moment, and numerous moments after that. Using the organ as an example (it's the instrument I'm most familiar with, though I can also play the accordion and recorder), t's not only the keys and pedals - you may need to change the stops and effects (ie. add vibrato to a particular section of the piece, or a different instrument's sound). There's a LOT going on at the same time.
When playing the organ, you're playing with at least two keyboards and a one-octave pedalboard. You're playing with both hands and both feet, and in addition to that you have to pay attention to the expression pedal (controls the volume) and whether you play with the heel or toe of your feet. And if you're playing a larger organ - the kind with four keyboards and a full console pedalboard, you also might have to shift your backside a bit on the bench, to make sure you can reach everything you need to reach. So it also becomes a balancing act.
These are things I had to learn when I was studying for the Western Board of Music practical exams. Since I originally learned to play by ear and prefer not to rely on notes if I don't have to, I crammed those Bach and other pieces into my memory - not only in my head, but also muscle memory. It took hours of practice every day for months on end, and was challenging - but there would come a point when everything would come together, and I can't really describe the feeling that creates. I was concentrating so hard, I wouldn't even distract myself by breathing.
And the piece itself actually wasn't that long. It was just a matter of having to train my mind and body to do everything correctly - many small steps that added up to a finished performance.
In the video of the violinist, I obviously didn't notice everything - I know nothing about violin playing - but I could see that there's a hell of a lot going on there - so many separate things the violinist has to be conscious of in the moment and in the future moments.
