Turns out the expansion port registers are found on addresses $2184-$21FF which makes them very similar to controller regsiters (adresses $4218-$421F).
The differences are quite important though.
One is pretty obvious: Instead of 8 arbitrary bytes with the controllers, we have 124 arbitrary bytes with the expansion port.
The other one is just as useful though: In practice (as in, on actual hardware), all 124 bytes can be changed at the speed of the SNES CPU. This means in theory you could set all 124 bytes to 0xA9 and start executing them. Then right after the CPU fetched the first byte you can change all 124 bytes to hold, say, 0x96. The resulting first instruction would be A9 96
Since the value can change every fetch of the byte, p4plus2 found the easy method to emulate it by just writing a byte buffer for all the bytes returned to the CPU as soon as it requires them. This is the expansionportdata
file you see inside the movie file, even though it's useless since it isn't read by the normal emulator.
In this movie a jump to the expansion port is used to write a program into memory (all in the last frame, so that it doesn't make the movie longer). This program then runs until it finally jumps to the credits.