They probably prevent it from starting and later do self checks (checksums), check for wine using other methods and then game-ban accounts in waves to hide how they detected cheating/wine.

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.