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

who doesn't know what Spider 2 Y Banana is and what to do on your route?

All kidding aside, some offenses are cakewalks.
One of my old high school playbooks went something like this:
3 digit series: the 1st number told us what kind of play it was going to be. Odd was a certain run, even was a certain pass and how you lined up and what route you'd run.

2nd number told us what gap the run play was going to go through. 1 = A gap, 2 = B gap, 3 = C gap, etc.
If it was a passing play, the number would coincide with whatever set

3rd number told us what kind of blocking it'd be. I think 1 was bootleg to the left or RB hits the left side.

So something like 121 Red was a running play (odd = run), 2 = B gap, 1 = left side; Red = FB hits the MLB that came through the hole.

Simple right? Imagine every playbook being different with some being harder. Once you get the lingo and what numbers mean what, learning the routes/blocking schemes are a lot easier.

Its the hardest on the QB because he has to understand every lingo coincides with where a potential receiver will be. Each position has it easier. I know during a 242 route, if I'm a WR lined up wide on the right, I'm just on a go-route and I'm his first option.

My QB has to know that route, and 3 other receiver's. A lot harder.

That's why ultimately low IQ QBs that don't practice or put much time and effort have a hard time grasping the playbook and ultimately these off-sync passes that get picked off more often than not. Smarter QBs minimize those mistakes because they know where their receivers will be, or in theory should be.