I wish I could think of a more interesting example, because I know there are plenty of games I didn’t play until way later, but the first one I can think of is Super Mario Bros.
I’m in my 40’s, so I was the right age for SMB when it came out, but after the Atari 2600 my family moved onto computers, specifically the Commodore 64. And while the C64 did get a lot of ports of arcade games, the closest thing it got to Super Mario Bros. that I played was a game called The Great Giana Sisters in 1987. But it wasn’t just that game but specifically a version of it that someone hacked to make the sprites match SMB. The original The Great Giana Sisters was already so close to SMB that Nintendo almost sued (I believe the threat of a lawsuit from Nintendo made the producers stop distributing the game to stores.) But copy protection was a joke back then, so it was easy to get games from friends or BBSs, and even modded versions like I mentioned. I can’t recall if any of the music was altered, but the game levels were already pretty close to SMB.
None of my close friends had a Nintendo either, and though I played SMBWorld once on a friend’s SNES, and got myself a Nintendo 64 in college and played Super Mario 64, it wasn’t until about 2003 that I finally played the original SMB on an NES. A girlfriend had one hooked up at her family’s cabin. That cabin was something they’d only be at like one week out of the year, and it seemed perpetually stuck in the '80s (or '70s in regard to the shag carpet). She could play that game with her eyes closed, but I barely managed to get through a few levels.
The game obviously holds up, it’s one of the all-time greats, but I didn’t grow up with it and didn’t have the nostalgia factor, so playing it 18 years after it came out didn’t blow my mind or anything. I also finally got to play Duck Hunt, but that wore thin much faster.
I think what makes this game not the greatest example is just that, even without playing a game like SMB, it was EVERYWHERE and sort of never went away. I never actually played it, but I still knew how to get to some warp zones, what enemies did what, where power-ups were, that the princess was in another castle. Of course, some of that knowledge comes from playing other Mario games, but there was a lot that was specific to the original that I just knew or expected.
If I can just remember some of them, there’s got to be a game that’s more obscure that I played years after the fact that still had some surprises to it.