Inspite of having such a large number of possible positions and games why do high level players bother about some specific game from some million years ago ? It may be helpful in understanding techniques and tactics but memorizing them seems very unusual. In fact memorizing games puts the person with more calculating ability at a disadvantage in time constrained games. Shouldn't the goal be to develop the chess aptitude rather than memorizing.
It's not as if top players sit down to memorize an old game. They don't spend time only memorizing, memorization is not a goal.
But they study lots of games. Old games, new games, famous games, their own games. Constantly.
And they have amazing memory so they remember these games, as a side effect of studying them, move by move.
Of course there are also players who don't quite study constantly, or who don't have amazing memory. But they tend not to become top players. Memory is very important in chess at the very highest level.
"Seems very unusual": source? Every time I've heard a good player (from club-competent to world-class) talking about his games, they were remarkably capable of precisely recalling positions. So I would say that
it is "very usual";
it stems from thinking long and hard about those positions, either during games or while studying;
it seems like a good trait, to the extent that I assume that a particularly good memory is a requirement for a good player.
When studying an old game, you can take however long you want to analyse if its the best move. The conclusion that this is the best move came from "calculating ability" and not from "memory".
There is not need to "calculate" this again when in a match. It's faster and easier to play from memory.
Kinda the same as when learning the times tables as a kid, you first learn to understand how they work. Then you memorize them for quick and easy use.
Memorization of entire games from a million years ago was never used as a method to train young players; or at least not those players who went on to become grandmasters. (There are other things that do end up taught repeatedly and usually mainly memorized, like crucial opening tactics and endgame strategies.)
It is easier, for a strong player, to memorize somebody else's game just after seeing it played out once than you might think possible, because chess has taught them the logic connecting the moves together. In fact they were likely able to predict many of the moves even before they learned which move was actually made in a given position.
A strong player will be good at remembering chess-like positions as well as sequences of strong (natural, logical) moves, and they will be correspondingly weak, compared to weak players, at remembering "positions" created by randomly positioning pieces on the chessboard, or poor, nonsensical, randomly selected moves. It is because every position objectively determines the strongest continuation or a few strong options, but there's often fifty more weak moves, including many that no player would normally consider in the given position.