I2C level shifting and protection
As I understand it, the zener diodes are meant to clamp the lines to a maximum voltage (5.6V in this case) to protect the devices on the bus, and is especially useful for long i2c transmission lines. Is my understanding correct?

This is probably correct, but without knowing where you got the circuit from, it's difficult to know exactly what they had in mind. Since the zener voltage is 5.6 V and the I2C pull-up voltage is 3.3 V, the zeners will have no effect on the circuit in normal operation.
Even on a 5 V I2C bus, the zeners would have no effect in normal operation.

Do I need clamping diodes if all of my i2c slave devices are on the same board, relatively close together?

Very likely, if everything is on the same board, you can simply omit the zeners.

What do the series resistors do, and do I need them?

In the original circuit, the series resistors were probably used to limit the current flow through the zeners in an over-voltage condition.
If you decide you don't need the zeners, you probably don't need these resistors, either.

The battery gauge IC allows up to 6V on its SDA/SCL pins, so is it ok to pull the bus up to 3.3V, even though the gauge is running at 2.5V?
Would it be better to level shift them to 2.5V?

I agree with your reading of the datasheet on this. Input high voltage levels from 1.2 to 6 V are allowed for these signals on this chip. Therefore there's no need to do any level shifting at all --- simply use 3.3 V pull-up for your I2C bus.