That console appears to be a 66-69 style console as it does not have the button for the glovebox door and is silver/black and not woodgrain. As for the cutout, the Hurst shifters have a jog at the base that require the console to be notched to clear the shifter and the Inland shifters go straight up through the center of the shift plate and don't need the notch. It appears you have the Hurst shifter. Is your car an original 4spd or was it converted?
Joe