Wine has a non zero overhead compared to Linux or Windows. Maybe one could come up with a mix of the Win32 API and Linux calling conventions? IDK. Or design something from scratch entirely, but then you have to write and maintain a translation layer like Wine for the rest of time :). Ideally one would take Wine and remove the overhead causing parts but keep most of it intact.
If the Windows program uses the Vulkan API, I imagine the Wine layer wouldn't be doing much work, would it? My guess is that the function-call conversion doesn't cost much on modern CPUs.
It's curious that Wine outperforms Windows on some CPU-intensive tasks, but is far slower for certain others. The article just gives the numbers, but doesn't give a deep analysis. Perhaps cache issues?