I very much doubt it. One of the causes of SAD is lack of enough sunlight, but this doesn't work as you might think. It's not light itself, but its effect on our body clocks that matters.

You need something that actually mimics the spectrum of the sun, because the cells that entrain (i.e. clock-tune) the chronobiological circuitry in our heads do not respond to the spectra of typical incandescent or fluoroscent lighting. That's why the special artificial daylight lamps cost more.

This matters because our chronobiological rhythms are strongly wired to day/night length, detected by entrainment. In other words, your sensors that detect day length are what tell you that it is winter, and that you need to be depressed (or hibernate, or migrate or whatever).

Video gaming is most likely irrelevant in this very low-level process. Unless of course you find a monitor that mimics sunlight.

See Russell Foster's "Rhythms of Life" for more.

My advice: unless it is debilitating and serious, enjoy your mild SADness as a way of being in tune with nature.