From what I remember when I stripped and rebuilt mine, the choke flaps rely on the spring, joining the 2 pairs together, to open and close. If the carbs are bolted back together slightly wrong, the shafts bind a little and the spring pressure can't overcome the friction, however, with a bit of manual assistance like in your video, they open. It may be worth slackening the bolts that hold the carbs to the retaining plates, just to see if they move back into line. Also, I seem to remember that the spring in the middle has to be wound under tension for one turn, before hooking it onto the mechanism. Very fiddly but can be done using a hook made from stiff wire, like MIG welding wire.
Maz
'76 CB500T
'75 GL1000 'Wing
'79 CB750L
'90 FJ1200
'93 GS500E
In a little place called Bexley, Kent, UK (Just south of London!)