(the video does not represent the actual clock, just an example).
The code, few lines in C, is in the magclock repo on my github account.
The idea is quite simple.
Three coils are controlled by the MSP430 in a sequence, like the brushless hard disk motors, same principle but much much slower.
Basically the system is designed to move a dented wheel one notch every second.
That wheel then controls the other gears of the clock.
The only thing is to have an accurate timing, so better to use a crystal on the MSP430.
This article give some other information about the MSP430 clock capabilities and settings.