Do I need to set up the diagonal D Pad directions?

Most likely, no. First, try setting up the gamepad without the diagonals. If diagonal directions don't respond, then your controller is special.

Some controllers are unable to have two directions pressed on the D pad at once. For instance, if you hold the D pad down and right, it won't report either down or right to Snes9x, it will instead claim a third, different, button is pressed: downright. This is known to occur on some XInput devices and Playstation controllers. You may be able to avoid this by switching your drivers from XInput to DInput mode or vice-versa.