https://bugs.winehq.org/show_bug.cgi?id=43775
--- Comment #14 from Matteo Bruni matteo.mystral@gmail.com --- Can you try to run HeroesSwitcher_x64.exe manually from the C:\Program Files (x86)\Heroes of the Storm\Support64\ directory (i.e. bypassing the Battle.net app)?
I suspect the game is started from a different working directory when run from the app and then it can't find the native DLLs stored there. That in turn might be a Wine bug but it might also be a Battle.net bug.