Some PC games are heavily DRM encumbered. Most (on Steam) are lightly DRM encumbered. Many (everything on GOG and other such stores) are not DRM encumbered.
This is a much better situation than on consoles, where all games are heavily DRM encumbered.
PC does not offer the same experiences Nintendo has. Animal Crossing New Leaf was only on 3DS and is one of my favorite games ever. It's depressing kids growing up after me won't be able to experience what I did as easily, I used to do local and online multiplayer all the time, I had almost every fruit in the game. Still play it now after getting another N3DSXL last Christmas after my old one was stolen.
You actually still can, just not on official servers. You don't have to break your device's or the game's security to connect to a third party server, the game just lets you. Unfortunately this is mostly a thing of the past, and most online games released in the past 5 years are completely unplayable without the central servers.
I really love how Velan Studios handled the shutting down of their game Knockout City.
1) They announced the official servers would be shut down months ahead of time with an exact date[0].
2) In that same announcement they also announced that they would be releasing a private server/client build before the shut down happened that would allow people to continue to play using privately hosted servers.
They delivered on the promise to release a private server build[1] and by the time the official servers were shut down, the community had already built out a hosted server solution complete with a custom launcher to support easily connecting to different servers.
Because Velan took the time to plan the games shut down properly and went the extra mile to produce one last release that included everything needed to run the backend, players were able to continue playing the game completely whenever they want.
I really hope that other game studios take similar paths in the future.