https://bugs.winehq.org/show_bug.cgi?id=42741
--- Comment #6 from Evtimiy Mihaylov evo@vaupe.com --- I can also confirm that the game works with wine-overwatch.
The easiest way to run it is by using Lutris.
After installing Lutris, install the Overwatch configuration from https://lutris.net/games/overwatch/
Skip the installation of the actual Overwatch game and wait for about a minute for Wine to be configured by Lutris.
Editing the "Overwatch" configuration:
1. Select the path to StarCraft.exe under Game Options / Executable
2. Under System Options, add new Environment Variable: Key: MESA_GL_VERSION_OVERRIDE Value: 2.1