I am having similar issues today, but not with all of the buttons of my wired-only Xbox 360 controller. On the day of launch, all of the needed buttons were functional, but after booting the game today, July 28, 2018, only the menu cursor control (left analog stick) and the previous menu/back function (B button) are working. I can't utilize the A-button to select any menu function, nor can I use the D-pad to scroll through areas like the mouse wheel does.
Nothing appears to be "selected" in Asphalt 9, unlike the "box" around a selection in Asphalt 8: Airborne, and I like the controller-cursor functionality, but if I can't select anything, I'm using the mouse anyway to work through the bug.