It's super impressive that people can play music like that form memory, I mean there's got to be thousands or tens of thousands of notes in there.

It is! Music is particularly amenable to chunking. The structure of measures, phrases, sections, forms, and pieces lends itself to efficient memorization or perhaps musicians/composers select/write more memorizable music with this structure in mind.

Actually, music was the only thing Clive Wearing can play, and he was suffering from retrograde amnesia--he could not remember his past at all. https://www.newyorker.com/magazine/2007/09/24/the-abyss

You can remember music like that too. Take any song you've listened to many times - I'm pretty sure if someone changed one note, or one word, you'd notice immediately.

Of course, actually playing those notes while you remember them is harder...

Eventually, it becomes muscle memory. At least for me, I start memorizing pieces from high-level to bottom, but eventually once I played it from memory too many times, I struggle to remember or recall high-level concepts and phrases and other things about the piece. But once I sit down and put my hands on the keyboard, it all comes back as I play through muscle memory.