I know this is an old thread, but its one of the many I have been over while trying to find a solution to this problem.
Mind you I'm running Steamlink as a port from RetroPie on a Pi4B 8GB.
Heres what I had to do to resolve the issue for myself.
In the Rapberry Pi Config file;
Disable Underscan
Disable Screen Blanking
Make sure Steamlink and other packages on your device are up to date.
Make sure that your Pi is outputting the same resolution or lower to your TV or monitor as the PC that the games are actually running on are outputting to its monitor. Eg. If your PC is running the games on a 1080p monitor, you likely wont be able to steam link from the Pi on a 4K TV @ 2160p without the black screen issue. I just set the display output in both my pi config and retro pie to 1080p to match my PC monitor and now Im playing without issue.
Hope this helps anyone whos still stuck with this issue.