re: How are NFL players able to memorize plays and recall them during games?

There are already some good answers in the thread. If you have "32 Scotland 5 Hook Right Mustang" as the play, only one part of that play applies to you and you know what to do.

Another advantage players have is that once you play football and practice, what looks like a lot of different pieces to an outsider is a single piece of information to you. They had some psych researchers do an experiment with a chess board. Participants were divided into two groups--regular people and chessmasters. Each person was shown a chessboard for one minute and then asked to recreate the game position. When the pieces were random, neither group did well. When the pieces were taken from an actual game position, the chessmasters did far better.

The reason is that regular people saw the game position as "white rook at A2, black knight at B5..." but chessmasters saw it as "Karpov defense vs. knight gambit (made that up, but the point stands.)