I think games probably destroyed my Note 2 battery. I often play games for hours straight while charging. Last Sunday it was dead with horrible heat. Then I borrowed friend's mpj backup battery, swapped it, and everything worked perfectly again. Now I have ordered a new battery online. I am not sure if playing games while charging could destroy the battery, if so, i swear wont do it again.
Charging and playing heavy games damages the battery very quickly. It is caused due to the overheating while charging, short Recharge n discharge cycles while charging n playing games and heat due to the GPU. Heat is the sole enemy of Battery. This is the same scenario in most of the mobile devices.
I recommend you to first fully charge the device n play until the charge drains out. I know it's a bit harsh.
I recommend not using your phone while charging as this can cause your phone to overheat. Also when you are using your phone while charging what actually happens is that the amount of time the battery actually requires for being fully charged increases due to simultaneous consumption. This can also cause the battery to swell and even hurt its life in longer run.