Is the gutter on the side of my roof dormer necessary?
Since the dormer extends out past the main roof, some (looks like about half) of the water would fall to the ground below. This could cause problems with drainage, puddling, erosion, and possibly lead to water infiltration.

The gutter should be there, but there should be a downspout running from the outlet to the lower gutter (as described in this answer).  As it is now, you will likely see deterioration of the shingles, where the water flows out of the outlet and across the roof. The rate of deterioration will depend on the volume of rainfall in the area, among other factors.