The frame on an arcade monitor is attached to the aquadag on the outside of the tube. Touching the metal frame of an arcade monitor is identical to grabbing the bare tube out of a TV set touching the back side of the tube. You cannot get shocked from touching this in either case, even with the monitor (or TV) turned on (!!so long as it is isolated from mains if it's on of course!!).
Assuming it's off, your only chance of shock on any monitor is via touching both terminals of a non-discharged capacitor at the same time. Since the picture tube is a large capacitor, touching either it's anode connection point and aquadag at the same time, or two connected points to a still charged (large) filter capacitor such as those on a G07 which can hurt more than the tube if they don't get discharged due to a blown fuse or other circuit failure.