Your DP is configured like it should be, as far as wiring types goes. Because the cable from the switch is so thick, you will have to put it through the clamp if it is too thick to pass through the notch in the motor wiring box. The line cord will fit in the notch and will be held by the wiring box cover. Inside the motor wiring box, connect the black and white wires from the line cord to the corresponding ones from the switch cable. Remove the ring terminals and use a pair of wire nuts, or insulated male and female spade lugs (I did the latter). At the switch, there are four screw terminals, two for the line side, two for the load side. Connect the black and white wires to the line side. Connect the orange wire to the load side terminal corresponding to the one with the white line wire. The red wire goes to the load terminal corresponding to the black (hot) line wire.. The ground should be connected to the switch frame, or put a screw into one of the unused holes in the left side of the head casting and connect the ground there. This makes a good ground to the drill press frame. Back at the motor, connect the orange wire to low/neutral/L1 terminal, and the red to the other terminal (this looks like it has already been done). Use the screw hole in the lower left of the wiring box to secure both ground wires inside the wiring box. And, you're done!
I have a bench version of this DP, about 1968 vintage. I tore it apart to the last nut and bolt in early 2020 and completely restored it. New bearings, a brand new chuck I had for a few decades went on, new wiring, and a new (used) table, since my original table was some sort of home/shop made thing that was not adjustable. I got an angling table from epay that didn't have much of an "arc of shame" from drilling through the work and into the table. I beadblasted and resurfaced the table, bead blasted everything else, and after a solid batch of paint coats, some new hardware, reconditioning old hardware, and some 'blueprinting' what I could that needed it, it came together quite nicely. In its day it was just a "utility' DP, but it runs solid and true much better than just about anything you can find today. I added a light about a year later. The motor on mine is a totally enclosed, fan cooled model with a side mounted wiring box.