The heat check is a very good indicator that Z17 is faulty especially if it gets hot within a minute and it's twin neighbor at Z16 stays cool and produces valid digits.
You can put one of the working displays onto the output of that Z17 chip - i.e. move the display at player 1 to the player 3 position and see if you now get legible digits.
Download the datasheet for the 7448 chip at Z17 which is a 'BCD to 7 segment decoder'. The logic datasheets usually have a truth table indicating how the outputs react based on the state of the inputs. That datasheet also lists all the output numeric display combinations which can help determine if it's producing valid outputs (presuming you have no connectivity issues from the MPU board to the display).
Any chance someone has socketed your Z16 and Z17 chips in the past so you can swap them around?