I know dohányzik is more common for smoking, so what would make someone want to use cigarettázik? Just to emphasize that it's a cigarette being smoked?
Basically, I guess yeah. There's also "szivarozik" for smoking a cigar and "pipázik" for smoking a pipe. And "cigizik" as a slang for smoking a cigarette.
Interestingly, since smoking cigarettes is the common thing to do, then you would just say dohányzik, and pretty much everybody would assume a cigarette so when somebody is smoking a pipe or a cigar we actually do specify most of the time.
I can see a pretty irritated smoker looking at his colleague who is reading something written on the pack of cigarettes instead of just taking one out and lighting it up.
It seems the "you" is plural so it would even be more than one colleague reading the package ^^