Welcome to the community.
You have a couple of issues here, as you said the "Exit" exits Bigbox, this is correct, you want "close active window" or similar wording to exit from emulators. As for Street Fighter 5, thats a PC game and should be exited through the in game menus. That is if you value your save games for PC games, the exit that can be set in Launchbox/Bigbox just binds your combo of choice to "Escape" on a keyboard, so that will be unlikely to ever exit any native PC games.