[1] e.g., https://en.m.wikipedia.org/wiki/NProtect_GameGuard
Of course, it's possible (if much harder) to go in and hack up the DLLs on Windows. Anti-cheat addresses that by whitelisting known-good MS hashes and/or requiring some type of signing. There's a lot more overhead involved in doing something like that for WINE, since every distro's build would be different, it's common for users to have their own builds with game-specific patches enabled, etc.
I've been out of the WINE scene for a while, but I'll say that I don't believe many WINE users are trying to exploit the platform to cheat. I think it's purely a cost-benefit tradeoff. The vendor doesn't feel supporting a legitimate WINE use case is worth the expense of figuring out a reasonable way to validate behavior, handle integration with distro builds, support debugging/custom patchsets, etc.
I would imagine Wine is in a similar predicament.
their method (blocking Wine) is questionable though. it reminds me of websites that block Central/Eastern European IP's "because of bots" (yeah, it happens). the goal is nice, but the method hurts many honest users.
There isn't a general way to prevent cheating on open platforms with this kind of game, so it ends up being a kind of cat and mouse game. Think of an aimbot (instantly moves your mouse cursor to an enemy as soon as the enemy is seen) or a wall hack that makes enemies visible behind obstacles. The only way to detect those is to check if your runtime environment is being modified by known methods. Opening a wine front (where you'd somehow have detect Linux processes/a modified wine or even a modified kernel etc.) is probably too costly compared to the number of non-cheating players on Linux.
The slippery slope of giving companies higher access is also seen in CSGO where (Faceit/ESEA, dont remember who exactly) put a bitcoin miner in their anti-cheat. Capcom put a rootkit into Street Fighter V to check for cheaters. Is that acceptable?
Incompetent, or rational decision in terms of bang-for-buck to reduce cheats?
Like another comment says, maybe it's easier to cheat using Wine, and thus banning the platform is faster/cheaper, even though they might end up catching a lot of legit users in this broad dragnet.