"Working a crowd" is unique. It has a social aspect that doesn't really apply to other situations where we would use the verb "work.". It can mean to shake people's hands, to greet people, to say things they want to hear, to make gestures that cause them to react, etc.

It is a way of saying, "doing intended action with an object." So when someone is "Working a crowd" they are "entertaining the crowd" or "keeping the crowd's attention". It is an idiom in English, meaning there is no real specific translation, it changes its meaning depending on the object that is being referenced.

BTW, why is it “working a crowd” and not “working the crowd”?

I agree with the others, but I want to add something. I would say that "working a crowd" means to keep them entertained and/or distracted, usually until some kind of event begins, or someone starts a speech, etc. The entire phrase is an idiom. Don't try to use "work the ..." with other words unless you know what they mean specifically. For example, "work a corner" could refer to a panhandler or a drug dealer or someone busking or a prostitute. It refers to a street corner, and it means that someone has set up at that corner to perform some kind of work. Just another similar example.

Most probably here it meant regulating the crowd