The circuit is designed so that it will not send signals through the breakout boards unless the EN input pin (at the upper right side of each board, which is shown connected to the blue wire) is connected to +5 volts. That is intended as a safety measure, to prevent the CNC stepper motor controls from being activated accidentally when the PC is powering up but is not under the control of Mach3 software.
The circuit uses a C4 Charge Pump Safety Board to apply that +5 volt signal to the EN pins of the breakout boards only when Mach3 is in control.
The Reset switch appears to be a manual override of the charge pump signal, which will permit the breakout boards to pass signals to the drivers even if the charge pump is not activated.
The way that the circuit is wired, the charge pump signal (and/or the reset switch signal) will only be passed through to the EN terminals of the breakout boards if the Stop/Manual Reset button connected to pin 10 of the LPT1 breakout board is engaged in the power on position. As far as interpreting pin 10 in Mach3, you would have to configure that within the software.
The Start button sends a signal to Mach3 on pin 15 of the breakout board connected to port LPT1. Some people use pin 15 for the emergency power off signal, but that should be configurable within Mach3.
The spindle output (normally open relay contacts) from the C15 could be used to switch the spindle power on and off. It is shown as being controlled by pin 16 of the LPT1 breakout board. Again, you can configure the mapping of pins to functions within Mach3.