I can confirm that i have the same issue here. It also affects Wolfenstein 2.
Same issue here.
And i add another question:
How can i play doom in 3 monitors? I didnt noticed any settings to do that, but is possible in windows.
From another user on Twitter:
Yes latest proton update also broke warframe on me too, i had to rename the wine prefix folder to create a new one
I had the exact same issue with DOOM and managed to fix it. I disabled the 2nd monitor, launched the game, readjusted all graphics settings (the update changed my resolution setting), exited then re-enabled the 2nd monitor. Relaunched the game and everything worked like before (without disabling the 2nd screen). Hope this helps.
I removed it and re-installed (the brute force method) and I can confirm it now works again.
Log (it's big): https://www.gamingonlinux.com/uploads/doom-ld.log
Perhaps comparing the log when it didn't work right, with the one above where it does may help.
@kiendang interesting to know that works, adjusting anything shouldn't be needed though if it worked originally, something with the Proton update changed it
Same here:
Ubuntu 18.04, GeForce GTX 1070 latest nvidia drivers installed.
Also facing the doom starts in a small box on second screen, display is cut and sometimes facing crashes. When I change the wineprefix with winecfg to use a virtual desktop, the game works but in a window...
An easy fix for this is to run the game in borderless window mode instead of full screen. When the game starts press alt-enter to put the game into windowed mode, then maximize it and change it to borderless window mode. There's no need to re-install the game or use a virtual desktop.
Has been fine since.
If you have issues in future try alt+enter to get into windowed mode.
Compatibility Report
System Information
I confirm:
Log file: steam-379720.log
Screenshot:

Symptoms
With a two monitor setup, as of the latest Proton update the game no longer displays correctly. Originally, it went on the correct screen in fullscreen. Now it goes on my second monitor, in a small box - regression. Worked fine in the original Proton release.
Reproduction
Get two monitors, set the left monitor to your primary. Try to run DOOM.