https://bugs.winehq.org/show_bug.cgi?id=45917
--- Comment #3 from Kimball kdt3rd@gmail.com --- So I have traced it somewhat more. It's definitely an issue with the fact that battle.net seems to set the process DPI awareness via SetProcessDpiAwarenessInternal / SetProcessDpiAwarenessContext / SetProcessDPIAware, setting it to "unaware" level awareness.
This can be easily replicated by changing something such as regedit to call SetProcessDpiAwarenessContext( DPI_AWARENESS_CONTEXT_UNAWARE ) at the start of winmain.