Ok not so hard. just a bit of work. The key to this is to recognize that you have 3 or 4 different kinds of animation elements.
I just want to avoid keyframing every part of the build up....
Well see the thing is even a plugin kindof keyfreames everything.
Amway you make things into functional groups for example the effect in the last video at 0.34 where the pillars and roofspilars come into existence. Very easy to do place the roof parts pivts in the right place select all the relevant parts in one go, rotate them straight (now if you select many things in maya and rotate the object in local mode each rotates in sync, but along its own axis), set key at straight and then at the end position (better yet do it in reverse), now you offcourse have parented theese to pilars hit arrow down key and move them local down key. Now the group may have hundreds of thousands of keys but its still just one operation. (work time estimated 20 seconds)
Ok now then you need s script that offsets theese keys sligtly randomly in time, no biggie to write but i have a examination tomorrow so im going to go and read (work time 3 minutes can be reused). I could do a demo but no time. when i have about 30 minutes to spare maybe. But im very busy.*
Same for other elements just get the gimic going all in sync then just offset the keyframes in time slightly to randomize the effect. Rince and repeat, each group takes after initial investements about 20-120 seconds per group. Be sure to set the objects local space when you build them this will make it way easier.
*offcourse if you must do this and tweak later you COULD make one set of keys for one pilar and then spread the same thing around the other parts witha wee bit of expression magic but why bother.