I haven't tried playing more than two blind games simultaneously, but I'm reasonably certain that I could play 3 against weak opponents, so maybe my input could be useful.
There's really very little active memorization that goes on. You do of course remember the score during the game (and usually for at least a few years afterwards, I'll explain why in a bit), but using it to reconstruct the current position is really the last resort: it's error-prone, takes time and effort, and generally means that something has gone a bit wrong.
You don't really memorize the current position either. First, there are general features that fit your existing knowledge of thousands of patterns: say, it's a Catalan structure with c6, except we ended up there from the Nimzo, a3 was followed by Bxc3 Qxc3, then he took on c4 and played e5.
This is an almost complete description of a complex middlegame position. To make it complete, you only need to remember a few pieces of information that don't fit the pattern: the rooks haven't moved except he's played Rfe8 already, h6 was played for some reason, we've exchanged on e5 so his knight is on e5, and my bishop is on d2, which means that e2 will be hanging in some lines.
Most of those features will change very slowly, and one at a time.
Here's the kicker though: after every move, you're calculating at least a little bit. In your mind, you're advancing the current position a few moves, going back a bit, going forward a bit, going back to the current position, etc. You're constantly looking at it from all sorts of different angles -- e2 is hanging potentially, so I know that I have a pawn on e2; it's hanging because Bd2 is shielding it from my queen on c2, so I know my bishop is on d2; I know my rook isn't on e1 yet; etc, etc.
In terms of memorization, this is absolute overkill for the tiny amount of information that you have to keep track of. And if you then analyze the game afterwards, you've more or less guaranteed that you'll remember it for years or decades. I have blitz games from last year that I still remember, and this isn't terribly uncommon.
tl;dr: you don't memorize anything when playing blind, it just happens automatically because reasons.