Hi Steven. Nice work getting the code even running. 
I don't know anything about the Mega unfortunately. What exactly are you connecting up here? It looks like the Densha-Do-Go controller acts like any other controller to the DreamCast -- so I guess it's just a matter of getting the four wires (power, gnd, clk/data1 and clk/data2) hooked up, like a regular controller?
It kind of looks like you can use those pins. Can you read from them and write to them from a sketch (ie print what digitalread reports when you have the pin at +Vcc and again when it's at gnd -- then hook up a led to one of them via a resistor and run a flasher sketch for that pin)?
Things to try in increasing order of difficulty: swap the two wires around, try different pins, connect up a logic analyser or oscilloscope to the data lines and see if "the lights are on".
Best of luck, let me know what works / doesn't work.