Hi there,
Like DM I would also think that this is a warning alarm, especially as it only seems to kick in when you are playing certain games. Easiest way to check for this is to go into BIOS and under the heading PC Health Status, check to see if the warning alarms for System Warning Temperature or CPU Warning Temperature are enabled. If these are disabled, are you running any software programs such as EasyTune? If yes, then check the alarm settings for overheating in these.
The only "Beep Codes" given by Gigabyte are for the BIOS during the initial POST sequence and these are not usually relevant once you are running in the Operating System environment. If, for example, the RAM was not seated properly then your PC probably wouldn't even start.