I'm not parent, but Overwatch runs very well on my computer with Wine + DXVK (Wine plugin(?) which translates DirectX to Vulkan). Performance is not noticeably worse than Windows.

Edit: I realize you may have been talking about HotS, not OW, but according to Google that should also work if you configure esync: https://github.com/lutris/lutris/wiki/How-to:-Esync

If you have a laptop with switchable graphics, you will need to use nvidia-xrun to enable Vulkan passthrough to the dGPU, but aside from that I just followed these instructions: https://github.com/lutris/lutris/wiki/Game:-Overwatch

Note that the Blizzard app will fail to launch with DXVK enabled, so you have to disable DXVK, launch Battle.net, enable DXVK, and then click the 'Play' button to start Overwatch. I made a few scripts for this, so I just do `./disableDxvk ... ./startBlizzard ... ./enableDxvk ... click play` to run the game.

  WINEPREFIX=~/.overwatch_wine/ setup_dxvk64 # enable DXVK
  WINEPREFIX=~/.overwatch_wine/ winecfg      # disable DXVK: delete the overrides from Libraries tab
  exo-open Battle.net.desktop # launch the Blizzard app, the .desktop should be generated on install