You forgot to divide by the volume of the vapour-cloud, there, as the hypothetical doorman is not getting his nicotine mouth-to-mouth from each smoker in turn.
This volume increases by the third power of distance--give or take a factor of 3 depending on wind strength and direction, it'll roughly be a cone of sorts.
So start with the quoted-above 2.25mg per hour of "in your face" nicotine, which we'll assume you could ingest if you keep breathing within a cubic foot (0.028 cubic metre) of a single smoker's mouth for the entire hour.
Say the doorman is standing 25m (~80ft) away. (if he lets a crowd of smokers gather much closer to his door, he's not really doing his job properly)
So that's distance times 80, meaning volume times 512,000. But it's a wispy wind-blown cone gushing in the specific direction of our poor doorman, so divide by 3, is 170,000 times the volume.
THEN, you multiply by the busy number of 200 people that are there all the time (very busy smoker's spot, this).
I get 2.6µg per hour. But only on the days when the wind has it in specifically for him. Standing within 25 metres from a crowd of 200 people constantly smoking e-cigs all day.