I found this:
It has directions for what to do in the event on black screen.
I ended up opening the game on Steam on a Windows device, activating the game, and then I could simply log in on my browser.
You would need to use Proton/Steam Play to install the Windows binaries of your games on the Linux system, then copy the install directories with the binaries to your Windows machine.
To install any Windows game on Linux, go to Steam settings in the category "Steam Play" and check "Enable Steam Play for supported titles" and "Enable Steam Play for all other ...
The thing here is that Nvidia deprecated 32-bits libraries in the .deb driver packages and the steam client is a 32-bits binary so it depends on the 32-bits libraries (just to be clear, the problem is not with the driver but with the libraries). There are several ways to fix this, the "theoretically" must recommended solution would be to download the .run ...
Since this thread still has no accepted answer:
A simple solution with Ubuntu 18.04 and possibly any later version that uses Gnome desktop is to just start the game (in full-screen mode). Then press the "Super/Windows" key and just drag and drop the game to whatever monitor you want to play on.
No need for "Big Picture" mode or anything at all.