I hope Ralston doesn't mind if I post an alternative to powershell. Powershell should work, but it's slightly complicated for non-programmers.
I would try a batch file (no guarantees but it might work). You can use taskkill to close programs out. You can use start to run programs and even have it wait until a process is done before the batch file continues. Here is an example that I wrote and tested. You would need to replace notepad with your game and maybe make other changes for Rainmeter, but it worked in my tests.
Copy/paste the below in notepad and save it as RunGame.bat. Create a shortcut to RunGame.bat and in the shortcut properties choose to Run Minimized (this hides the command prompt window). Tip...