I've looked at that vid and so far I have only come up with 2 ideas as to what it might be. One is that your base plate gasket is old and leaking and it just looks like it is leaking from the choke. However, maybe my eyes are playing tricks on me with that video. Idea number 2: the air for your choke is being pulled from the bowl vent in the front of the carb
(I cant see the front of the carb so this is just a guess) remember the hot air chokes had vacuum applied to them.