Same here, haha, between my early days of game collecting and then Steam sales fever, I have so many more games than I'm realistically going to be able to beat. Plus I'm a bit of a datahoarder, so I have everything either on physical media, and the respective console to play it, or backed up on drives, and I plan to further improve my storage in the near future, so even if Steam or the entire internet goes down, as long as there's electricity, I'm good
Assuming Steam survives, or your console manufacturer keeps releasing updates, or whatever.
In the cartridge days all you needed was the console and the cartridge. As the years go by, you rely more and more on online services, software updates, and so-on. Even for supposedly offline single-player games, many of them stop working eventually.
Well, Valve did say if they ever close shop they'd offer all your purchased games as downloads without DRM. Not that it will ever go that far.
Even in the cartridge days if you played on PC you had to download patches from the developer website.. which as you can guess nowadays is no longer available. There was also SecuROM which bricked several games as the activation server no longer exists.
But sure, if we go all the way back to Super Nintendo and Nintendo 64 then those games will survive the apocalypse. Many PC games even from that time wouldn't (at least not fully patched and you might scratch a disk).
The "cartridge days" is a very loose term. Nintendo 64 used cartridges and came out in 1996.
And lol, "there were no PCs", Atari came out in 1977. PCs have been around a lot longer than cartridge game consoles (NES was 1985). The internet also went live around 1983, so even that happened before the NES. Though public domain only happened in 1993.