I checked out the Instructables you linked to get an idea of how the LED Cube is animated. It looks like that author is writing to raw registers to change the LED states instead of using the traditional
digitalWrite commands in order to save a few execution cycles. That sort of implementation is going to be orders of magnitude faster than Tessel's JS interface.
SPI is often used to generate a sort of high speed signal but I don't think it's applicable here because you're writing to something like 20 different GPIOs. SPI can output a high speed signal only one pin.
I'm not sure this application is currently possible with high frames per second on Tessel without writing a bit of C code. We do have a tutorial for writing C code that interacts with JS that should make it fairly straightforward.
@kevin do you have any other insights into what might be possible here?