This is a simplified explanation:
The mAh (milliAmp-hours) rating is how much energy the battery holds before going dead.
The Voltage is how much energy is being put out at any one time.
With alkaline batteries, the voltage drops steadily as the mAh is drained, until the voltage isn't enough to power the device anymore. The battery might still be useable for other things that require less voltage (When a digital device "runs out of batteries" try putting the "dead" alkaline batteries in a flashlight...it won't be as bright as it would be with new batteries, but it will still work)
With NiMH batteries, the voltage remains mostly constant as the mAh is drained, until the MAh is almost depleted. Then the voltage drops relatively suddenly, and the voltage isn't enough to power the device anymore.
Undervoltage (2.4v total instead of 3v in the case of the GP32) won't damage electronics over time. Overvoltage could possibly damage equipment, but it would be pretty difficult to supply the GP32 with too many volts with batteries.
I use 1800mAh NiMH batteries, and I'm very happy with the battery life I get. Using 1300mAh batteries will work fine with your GP32, but they will go dead faster.