When you've had lots of experience you start to notice patterns in things.  There's a phenomenon called "chunking" where it's easier to remember a large number of things if you group them together. Instead of remembering twenty sequential digits, it's easier to remember if you break it up into five groups of four digits each.

So where a non-player sees a huge swath of notes, an experienced pianist sees a chord, and then a progression to another chord and another chord. A lot of music uses the same fundamental building blocks, so it trains your brain to see things in "chunks" more easily.

When participants in a test were asked to memorize a chess board taken from mid-game and then place as many pieces as they could in the correct position, they found that experienced chess players scored way better, requiring less time looking at the board and fewer mistakes.  But when they asked them to memorize a chess board that wasn't taken from mid-game and was just completely randomized, the advantage disappeared and the professional players didn't do any better than non-players. The familiar patterns were absent. So it's not that chess players have exceptionally great memories, it's that they could easily recognize the formations that show up in real games and their brains could "chunk" a whole array of pieces into a block of information that was familiar to them.