MELE PC game won’t stop running.

An additional detail:  You don't need to run any of the games for this issue to occur; just starting then exiting the launcher is enough to reproduce the "still running" issue.  And yes, I did verify that nothing related to MELE was showing as running in the Task Manager, aside from the OriginWebHelperService, yet Steam still showed MELE as still running.

All of that said, I did figure out the cause of this issue:  Origin.

I already had Origin installed on my machine before installing the Steam version of MELE, and apparently it doesn't like that arrangement.  Uninstalling Origin, then running MELE from Steam and letting it reinstall Origin, completely resolved the issue.

It seems I spoke too soon; uninstalling Origin resolved the issue once, but it's still recurring.

Just for the heck of it, I tried opening Origin while Steam was showing MELE as still running (even though it wasn't, and had only started and exited the launcher), and noticed a banner that says "The Origin store is currently disabled because it was launched from another application."  Trying to exit Origin results in what you see in the attached screenshot.  So, apparently, it's not just Steam that thinks MELE is still running, but Origin as well.  Opening Task Manager and doing an "End Process Tree" on both Origin and steam will resolve the issue, but this is far from ideal.