So I know nothing about this board beyond what I've quickly googled.
If I understand correctly the Multiwii project (on the hardware side) started out basically marrying wii COTS components with an arduino. The software side, flashes a flight controller application onto the arduino which then can talk to RC components to control motors and servos, all with the intention of controlling a multi-rotor copter.
The board you linked to directly appears to be an arduino with a gyro/accelerometer on board, specifically the MPU6050. So you should treat it as such. Forget about the Multiwii software, it's not likely to be of much help beyond possibly showing you how they interfaced to the specific sensors on the board.
To learn how to use the I2C interface on the DSC, I would suggest searching the CD forums for "I2C". There have been quite a few good discussions on the topic within the last year. There are even some posts on specifically talking to arduinos through I2C.
Then I think you're going to have to basically replace the stock firmaware on the board you bought. You should be able to use the arduino IDE to reflash the board with your custom code.
Your going to have to write your own code to interface to the sensors. Or, since the multiwii code is open source, you may be able to take a look at how they interface with the sensors, and just gut all their flight controller logic.
Once you can talk to the sensors through the arduino, then it should be pretty easy to take the data and push it out of the i2c interface.
You should be able to find examples of how to use the i2c libraries on the arduino website.
Here's one there may be better ones. It looks like you need to use the
Wire library. Note, you might need to modify the library to match the pins that your i2c interface is actually physically wired to. Your board is running on an Atmega 328p.
This page may or may not be helpful.
This is all a guess on my part. Should be a fun little hack. I'd be interested in how it turns out. If we end up at the same regional next year, I'll try to come over and find out how things went. Hopefully districts don't mess that up too much.