As a former cheat developer, I think it is impossible since it is digging into some specific stuff of Windows. For example, some anti-cheat uses PsSetCreateThreadNotifyRoutine and PsSetCreateThreadNotifyRoutine to strip process handle permission, and those thing can't be well emulated, there is simply nothing in the Linux kernel nor in the Wine server to facilitate those yet. What about having a database of games and anticheat that does that, and what if the anticheat also have a whitelist for some apps to "inject" itself into the game process? Those are also needed to be handled and dealt with.
Plus, there are some really simple side channel exploits that your whitelisted app have vulns that you can grab a full-access handle to your anticheat protected game, rendering those kernel level protection useless, despite it also means external cheat and not full blown internal cheat, since interal cheat carrys way more risk, but also way more rewardings, such as fine-level game modification, or even that some 0days are found on the game network stack so maybe there is a buffer overflow or double-free, making sending malicious payload to other players and doing RCEs possible. (It is still possible to do internal cheat injection from external cheat, using techniques such as manual mapping/reflective DLL injecction, that effectively replicates PE loading mechanism, and then you hijack some execution routine at some point to call your injected-allocated code, either through creating a new thread, hijacking existing thread context, APC callback hijack or even exception vector register hijacking, and in general, hijack any kinds of control flow, but anticheat software actively look for those "illegal" stuff in memory and triggers red flag and bans you immediately)
From what I've seen over the years, the biggest problem for anticheat in Linux is that there is too much liberty and freedom, but the anticheat/antivirus is an antithesis to liberty and freedom. This is because anticheat wants to use strong protection mechanism borrowed from antivirus technique to provide a fair gaming experience, at the cost of lowering framerates and increasing processing power, and sometimes BSOD.
And I know it is very cliche at this point, but I always love to quote Benjamin Franklin: "Those who would give up essential liberty to purchase a little temporary safety, deserve neither liberty nor safety". I therefore only keep Windows to play games lately, and switched to a new laptop, installed CachyOS on it, and transfered all my development stuff over to the laptop. You can basically say I have my main PC at home as a more "free" xbox.
Speaking of xbox, they have even more strict control over the games, that one of the anticheat technique, HVCI (hypervisor-protected code integrity) or VBS, is straight out of the tech from xbox, that it uses Hyper-V to isolate game process and main OS, making xbox impossible to jailbreak. In Windows it prevents some degree of DMA attack by leveragng IOMMU and encrypting the memory content beforehand to makd sure it is not visible to external devices over the PCIe bus.
That said, in other words, it is ultimately all about the tradeoff between freedom and control.
A similar concept, trusted computing: https://en.wikipedia.org/wiki/Trusted_Computing