Have you tried plugging your Pi into different inputs? Some of them don't play well with certain resolutions or signals, so maybe the games display in a different resolution than your menus, which would explain why you only have problems when launching a game.
For instance: I have a Marantz with a front aux port which doesn’t display the SNES Mini Classic. All back inputs do.
A friend has an older Denon AVR that has this problem on all but one of his back inputs... I remember reading the reason behind this functionality, but can't recall exactly what it was.
Tldr: try different inputs