It sounds as if the doctor is doing a cycloplegic refraction for your son, which is needed in children to obtain the proper prescription. The prescription is measured after the dilating drops relax the pupil and prevent the eyes' natural focusing or accommodating muscles from working. If the prescription shows a significant difference between the 2 eyes, then it is important for your child to wear the glasses, to prevent the development of amblyopia (lazy eye) in the eye with the stronger prescription requirement. Patching of the better eye for a time might also be needed. If the eye doctor is not a pediatric ophthalmologist, you might consider a consultation with one for a second opinion. Limiting his computer games will not improve the vision.
Thanks a lot for your expert opinion.