Just watched the video - that's a pretty cool project.
Alternative to steppers: DC motor with encoder.
32 of them is too many for a single Arduino, even a Mega. It's also not scalable that way, better break it up. One possible approach: make multiple modules based around single Arduinos. 4 motors on one Arduino, which reads the encoders and handles the direction and speed of the motors.
This way you can build your own PCB onto which you can easily solder a Pro Mini and motor drivers, and have connectors for the power supply, motors and communication with the other modules. That would make it fairly scalable, mostly subject to your power supply and communication speed/distance limitations.
One master which sends high-level commands to the various modules - such as speed, direction and distance to move each motor. I2C comes to mind as communication bus if it's not too big a structure. Serial is another option, but slower.
You have to write two sketches: one for the slaves (receiving communication, controlling the motors), one for the master. The master may be an Arduino, but you may also use an RPi, afaik they have I2C.