It's not like they accidentally memorised them after they see the game once.
I can't make an informed opinion myself, but I can retell the arguments I've heard used.
In the past, players like Bobby Fischer dominated their peers, winning tournaments by 5 games or more. Today, super grandmasters play 20 moves of prep from memory and agree to a draw. When they get out of prep they don't play as skillfully as players of the past, pre chess engine era. Today super grandmasters put all their attention into opening theory. (I'm retelling the arguments I've heard, these aren't my own opinions)
I will say I much prefer to watch a super grandmaster blitz or rapid game over a classical game. Not that I watch them live, but I see the occasional video of a grandmaster analysing them in a 10-30 minute video.
https://content.iospress.com/articles/icga-journal/icg0012
But I also think that in a metagame with less equality out of the opening and more blunders, skill was more rewarded in the past - so just look at Magnus’s blitz rating to compare. Either way, the fact is this year Magnus _did_ regularly dominate his peers, despite them all having big teams with thousands of CPU/GPU hours of prep behind them. I know Ben Finegold is never going to be convinced but whatever.
Check out this recent short video of Magnus being shown and recognizing positions from Vishy Anand games.
https://www.youtube.com/watch?v=acVvkz4MsKc
Common might be recognizing the opponent and next move (I, patzer, got half right, also that the move against Lautier was h6!), but Magnus also remembers the year, tournament, most of the game etc. He has a remarkable memory, and studies a lot of games, past and present – because he loves doing it.
Bobby Fischer was similar, from what I hear. I've read quite a few stories of people from around the world meeting him and he'd say "I liked your game against X 10 years ago but you should have played move Y" and they were amazed he'd even heard of them, let alone studied their obscure games. (This was pre-internet and pre-computer-analysis)