Doing the math I guess the Game Gear is drawing roughly 9V (1.5V x 6 assuming they are run in series no parallel) from the AA batteries so in theory a 9V battery would work, but at 1300 mAh it isn't any better than high end AA batteries capacity wise. The Game Gear draws about 300 mA so you are looking at a little over 4 hours off of that battery. You could run 2 9V batteries in parallel to get about 8 hours of run time, but you would have to rewire the Game Gear to do this.

The CleanJuice rechargable battery mod (pretty easy mod with no soldering required) or some 2400 mAh or higher (2850 or 2700) rechargeable AA batteries would both be better options than rewiring the Game Gear to run off of two 9V batteries though.