Have a look at this
Planet CNC ? View topic - CNC 3020T
On your picture of the bottom side I think I can see a PIC controller this makes me think your controller is such a type.
The input for signal is the USB port and not the parallel port. It will not work with Mach3
I expect the parallel port is used for connection of a extra axis and input for the limit switches etc.
Install the supplied Planet software and check if it recognizes the board. If so, you have to find documentation about the parallel connector.