Anti-cheat is a misnomer; it's much more about detecting cheats more than it is preventing them. For people who are familiar with how modern anti-cheat systems work, actually cheating is really the easy part; trying to remain undetected is the challenge.

Because of that, usermode anti-cheat is definitely far from useless in Wine; it can still function insofar as it tries to monitor the process space of the game itself. It can't really do a ton to ensure the integrity of Wine directly, but usermode anti-cheat running on Windows can't do much to ensure the integrity of Windows directly either, without going the route of requiring attestation. In fact, for the latest anti-cheat software I've ever attempted to mess with, which to be fair was circa 2016, it is still possible to work around anti-cheat mechanisms by detouring the Windows API calls themselves, to the extent that you can. (If you be somewhat clever it can be pretty useful, and has the bonus of being much harder to detect obviously.)

The limitation is obviously that inside Wine you can't see most Linux resources directly using the same APIs, so you can't go and try to find cheat software directly. But let's be honest, that approach isn't really terribly relevant anymore since it is a horribly fragile and limited way to detect cheats.

For more invasive anti-cheat software, well. We'll see. But just because Windows is closed source hasn't stopped people from patching Windows itself or writing their own kernel drivers. If that really was a significant barrier, Secure Boot and TPM-based attestation wouldn't be on the radar for anti-cheat vendors. Valve however doesn't seem keen to support this approach at all on its hardware, and if that forces anti-cheat vendors to go another way it is probably all the better. I think the secure boot approach has a limited shelf life anyways.