https://bugs.winehq.org/show_bug.cgi?id=41951
--- Comment #3 from Mathieu Comandon strider@strycore.com --- Someone suggested trying out setting bcrypt.dll to native. I have tried that and bcrypt fails to initialize but that's maybe because I'm using the wrong version of the dll. Specifically, I'm looking for a proper dll from Windows 7 64bit.
@Johannes have you tried the 'devMode_enable' option as stated in the error message? Setting this will disable multiplayer and taint any existing save games but getting the game to launch would be a start.
You can try setting it in $WINEPREFIX/drive_c/users/[username]/Saved Games/id Software/DOOM/base/DOOMConfig.cfg