That's one view, but I'd argue that they are both variations on the general problem of "how to run software on a computer without letting the owner of that computer actually control the software". When it's against piracy, the goal is to make sure that the software can refuse to run if it's not correctly licensed or to make sure that the user can't send its output to a recording, and when it's against cheating the goal is to make sure that the user can't modify or view the game state except through the standard game UI, but both revolve around denying the user power over software executing on their hardware.

The big difference is that anti-cheat usually applies on company property, i.e. on their servers. The most common punishment for tripping anticheat is a ban from online services of some kind.

That's true but I was referring to games that continue to add new features and improvements to their Windows client, but leave the Linux client on an old version, which is a separate issue. With online games this sometimes even means that Linux users will no longer be able to play with Windows users https://www.lustvollerjonas.com/ .

On the other hand Wine probably has better backwards compatibility with old Windows games that Windows does in many cases.