Just to be clear, I have crashed my Mill many time. Most of the time, it is easier to get to the E-Stop on the Mach3 screen than the big button on the switch box.
As for you wiring. My assumption is that the terminal blocks are electrically connected from top to bottom. In other words, if a wire is connected to the screw on the top then it is electrically connected to any wire that is in the screw directly below it. This is a typical expectation for terminal blocks but I will go and check mine later today just to be sure.
Based on that assumption
Connections 1;2;3;10 are all connected together and then in turn connected to one side of the E-Stop switch ("From Estop"). You show that the wire labeled "To Estop" is not connected to anything. I goes to the bottom of the terminal block but there is no second wire on the same screw and there is no wire on the screw directly above. Not sure what to make of that.
I would be curious if you go into Mach3 "Ports and Pins" config screens and look at the "Input" tab, do you see the entry for pins 1,2 & 3 ? What does Mach3 think these inputs are for?
I don't think it would help for me to check mine as it is clear we have different controller boards.