Since the screw looks like it has a good sized head, you could try gluing (araldite) a similar screw to it, upside down. When set really hard, 24 hours at least, araldite has pretty good shear strength so a pair of pliers on the upside down screw might then turn it. Degrease it first, for a good bond.
I don’t think I’ve ever tried that, it just looked like an option. You’d need to be extremely careful to make sure the araldite does not squish out and spread between the screw and adjacent case, making matters much much worse....
You could also try aralditing an old screwdriver bit to what is left of the screw but that’s less likely to work, lever’s law working against you.