Wow, that's just evil.
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?
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.
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.
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.
[1] e.g., https://en.m.wikipedia.org/wiki/NProtect_GameGuard
I would imagine Wine is in a similar predicament.
It seems far more likely to that most players are just using Wine for its intended purpose—to play Fortnite on Linux.
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.