Depending on what kind of sound you are looking for.
If you are looking for Thumping (Kick drum Bass) type of bass I would point the subwoofer towards the internal cabinet wall and have the port vent out a whole in the back of the cabinet. This will make the cone of the subwoofer travel more (back and forth) The wall that you the subwoofer firing towards I would glue a piece of egg crate foam. To keep the accoustics sounding decent and not muddy (so you don't get that bass slap sound)
If you want less of a thump and deeper bass (jazzy type of bass) just turn the subwoofer out a vent through the back and have the port aiming towards the cabinet's inner wall. This will keep the Subwoofer from moving as much and gives it more of a controlled bass.
Make sure everything is tight as well on your cabinet because with a subwoofer that size it is going to rattle your cabinet. Especially your control panel. You can line the cabinet with egg crate acustic foam to help just keep it away from all the components in your cabinet that get really HOT. Like the power supply and monitor wire area.
Using a subwoofer and firing it downwards the floor would work and use the arcade cabinet as an enclosure works well for space. So basicly you will have to buy a subwoofer at like radio shack or some place that runs at 8ohms. Just like what they do with Pinball machines.
Remmeber you are putting an enclosed subwoofer into another enclosure. Volume of air and cubic space all come into play when dealing with bass.
I can go on and on but hopefully what i said made sence. I typed it out fast and didn't proof read it

I would test it out and move it around before mounting it or cutting or what not.