Well one problem was that it wasn't even really implied that the slur you censored was even racial. By the time you mention "same side of the race equation" the story is pretty much over. So yes, while on second (or multiple) readings there is about enough information in there to work out what was going on, the fact that you left the crucial hint until right at the end makes it look like the reader is not meant to realise the full picture until that point And even then you can only really deduce that he's non-white, not necessarily black (which may or may not be enough I suppose). Which in turn makes it look like that's part of the question/test. If it isn't, then why not just clearly state "the store detective guy is black" when you first introduce him?
Well I did also outline other things that confused me about the question, such as the fact that, as worded, there didn't seem to be any indication that anyone else in the scenario was about to be violent, which would imply that the question is about whether or not I would initiate violence in response to a verbal insult. But then maybe I misread it and you were implying that things were about to "kick off" anyway, in which case the question is then about how I would react to that. I also didn't get why there was the implication that the police would be appearing on the scene, since nothing had apparently happened that would warrant that at that point. I also don't know if your question is specificially "would you punch a racist guy" or a more general "would you punch a jerk".
Anyway, if you want a direct answer it is that no, I wouldn't just spontaneously punch a guy in the face just for being a dick to someone else. I don't see why that would be a good thing to do.