I'd bet all the marbles that they're "JIT" rendering the full video upon request. Intro + hour chunk (12 options) + minute chunk (59 options, skipped if minute is 0?) + am-pm chunk (2 options) + Outro. If you open the page in two different browsers at the same time and chose the same pill color, the resulting video file URL is different; this suggests to me that they're not caching the compilation results for the next client.
I would have strong doubts that they are rendering them each time. I would put all my marbles that they have each one pre-rendered 1 time, and then paid Keanu to sit in a booth and count from 0 to 59
