Actually, the firmware IS on the miner, the mcs file you're talking about flashes onto the board that controls the two blades in each Avalon. The RPi has a separate 'firmware', which is as you described.
I2C is a hardware protocol - one of the two most common ones (SPI being the other). It's just a standard way of hardware talking to eachother without a bunch of overhead or buffering that would typically be required for something like Serial. The only real downside to these kinds of protocols is that they require immediate processing and generally can't be on very long cables.
The CGMiner software is on the RPi, in the other image - completely different from the MCS. Think of it like this, CGMiner is like a conductor in an orchestra, and the Avalon is like a musician - this is even more apt with the Avalon, since you can connect multiple Avalon's to a single CGMiner.