To improve navigation for people coming across this thread: The restarting of game client apps by starting a Windows process is now supported. The Process.Start API in .NET Core can be used in a volatile host to start a new Windows process.
To find out if a game client process has exited (so that you know when to start a new one), you can use the HasExited property.
(To make it easy to get the newest updates, I post about new features and improvements in the thread BotLab Devlog - #26 by Viir)