From the video, it seems like the houses were cut from the original foundation and a huge blocks
of concrete was formed underneath the houses. Before pouring the concrete, they dug under the houses and inserted metal framework for the move, that was likely how they lifted the whole thing to insert the jacks later on. The process of doing this seems way more interesting to me than the final move with these synchronized jacks. I'd love more details about that
Search youtube for "crawl space underpinning" for some videos of a residential process.
I'm sure they're doing something more elaborate there, but in residential you do this underpinning technique if you want to replace or extend your foundation (in my case, putting a basement where there is a crawl space), where you mark the foundation into 2' segments and label them A, B, C. Then you go through and dig/cut out all the "A"s, and pour footings and foundations in place, then repeat for the Bs and Cs. I'm thinking about doing this for my crawl space just to have some more space for storage.