I think you’re mistaken there.
Wine is a vanilla Linux executable that runs as the user who launched it. The Windows program it runs thus also runs under that user. That’s possible because Wine doesn’t do anything system-wide (like intercepting calls or anything), it already gave the process its own version of i.e. LoadLibrary()
(the Windows API function to load a DLL) and can happily remap any loaded DLL to Wine’s reimplementation of said DLL as needed.
Here are, for example, the processes created when I run Paint Shop Pro on my system (the leftmost column indicates the user each process is running as):
Also, some advice from WineHQ:
I don’t know why that comment is collecting downvotes. They are referencing George Orwell’s “Animal Farm.”
Context: “Animal Farm” is a story about how communism can devolve into dictatorship. In the story, the animals on a farm drive out their tyrannical drunkard farmer. They write on the barn wall: “all animals are equal” and live in communist utopia. But some animals, too, hunger for power and status. Rather than overturn the system, they undermine it by adding “…but some animals are more equal than others” to the barn wall, legitimizing a ruling class (themselves) because they are “more equal.”