Interesting video.
Every building is different. Some I take down board for board. Some I cut the complete walls into ten foot wide sections, then haul the sections home by stacking them up like pancakes on the trailers (In Ohio you don't need permits at 10' wide. Bigger than that and it can get expensive). Some others I cut the corners and lay the whole wall down, then just pick them up and load them. I've never used cranes or scaffolding, just do it all by hand, ~along with the help of tractor jacks, come-alongs and broom sticks for rollers, and occasionally gin poles I set up. I've moved and rebuilt and restored somewhere around 40+ buildings, including two houses, a number of barns, two forty foot silos made of 2 1/2" chestnut, and a couple of windmills. Generally I do 3 or 4 buildings a year.
I mention all this because in the video the folks took off the siding and then removed the roof. I guess that's ok because that was a relatively small barn. And like I said every building is different. But usually I take off the roofs first. I find that usually the siding helps to keep the barn stiffer and more safe when peeling the roof. When the siding is off sometimes the structure can sway pretty good. Another thing I noticed was that in the video, they let the main beams free fall. It didn't look like they cracked. But it happens. Usually it might be better to lower the beams, if you are going to reassemble the building. Nice job though.
I've kept most of the buildings I've moved, and used them to establish a village. The museum is open and free, seven days a week/daylight. Stop by anytime. Some of it you can see on the website:
www.ohiofarmmuseum.com