So I got the game to run… the quick and dirty way I did it was to use Lutris to install Overwatch. It will basically install Battlenet and you can choose to install Overwatch or not, I only want the wine-prefix it created.
I then choose to run an exe from within the prefix, choose the 1.30.2 version installer. It will install successfully and then I also got the grey screen. I moved the windows out of bounds of my screen and back into view which refreshed the content and I could click on Digital version (and not CD-Key). Move out of bounds and back and I can enter my Battlenet credentials. Move out of bounds and back and I can verify my account etc. etc…
Game launched fine, was stuck at 1024x768 but I am sure someone here knows the fix for that
edit: Manjaro 18.x
nvidia 1060
410.x driver