I use the Game Launcher and like that it adds new games automatically. Personally I've never used the DND feature of the app but if it was an option and it was taken away in one of the last updates there isn't much that can be done here. You would have to contact the app developer through the link on their app page.
Since it is basically a DND function you could use Bixby to turn on DND.
Go to Settings, use the search bar at the top to locate and open DND.
Set DND default time in its settings.
Press and hold the Bixby button until Bixby is listening and say, Show my Bixby routines.
Press the + sign and choose "App opened". Then select Game Launcher and press Next.
Press the + sign and choose Do Not Disturb, it will ask if you want to turn it on or off.
Then press done.
Now when you open the Game Launcher DND will be turned ON and should run for the selected time you choose.
It's not perfect but it will accomplish what you wanted.