It's nearly every game, without fail. Whether it's a MAME rom or something purchased from the Polycade store, hitting back will always bring up the "Pausing" screen, with a spinning windows "thinking" icon. Tapping the joystick will move to the "resume/exit" screen, as if AGS was waiting for some input.
I'd also note that when I launch AGS, I don't see the spinning mouse cursor. But after launching and existing a game, the cursor some times persists.
Images here. https://imgur.com/a/liWqidX