Replace light switch with no ground wire in box
Pigtail the ground to the box

It looks like the original installer did a pretty sloppy job of installing the cables (the damaged "redhead" insulating bushing top left is evidence of that").  That aside, the BX armor should be grounded, so by extension, the box should be grounded via the armor.

This means that you should connect the ground screw on the switch to a 10-32 machine screw threaded into one of the holes in the back of the box using a bare or green #14 wire pigtail.  Your average big-box store will carry pre-made-up ground pigtails that you can just screw into the back of the box then attach to the ground screw on the switch, or you can make your own with a 10-32 machine screw and a length of 14AWG wire that's been shucked of its insulation by looping one end of the wire around the screw.