How should I connect a grounding wire from a device to this box?
That wiring is AC cable, modern AC cable. I can clearly see the bonding strip that makes the sheathing a grounding conductor. So since a grounding means exists you must use it.

With switches, simply screwing them to a grounded metallic box grounds them, as opposed to a receptacle which would need to be a self-grounding type. So technically, just installing the switch would be adequate, but since there is a ground wire from the dimmer I would connect it to the box.