Staring at a screen/computer/hand held games... dries out the eyes. It then gets sore. Because, when one is staring at a screen, they do not blink as much.
Also, the lighting on the screen, can be too bright or too dim. Hence the eye is straining as well.
Same for reading.
Or you go and get a 2nd opinion, with an Opthamalogist.
Or, try and get him eye "moisture" drops.
Also, doing things like that, is only near sighted things. Seeing things up close. For the eyes, only doing things like that, is not good for the eyes. A child, ALSO has to do things, that entail far vision things. Just putting away the hand-held things, and going outside etc. So that the eyes are not only forming and seeing, up close things. My Husband read about this, recently.