The rules specifically say the controls can be displayed outside of the game. This is primarily for mobile with touch controls to have buttons to press. The other technical mention, that you might be thinking of, is that the game can have border art outside of it as long as it isn’t rendered by the game.
The buttons to the side are fine, but your game is displaying information about itself outside of the 64x64 pixel restriction. The inventory, stats below, and the text over the 64x64 display don’t follow this rule.