I think those rates have more to do with motive than gun control. Detroit is literally broke, and the unemployment rate there is quite high (correct me if I'm wrong). It's a rather poor place, which causes crime rates to be high there, including murder.
The trends of unemployment and wealth imparity/disparity are the main factors that causes these high murder-rates. And it's the same for all those high murder-rate countries, they all have a huge wealth-disparity problem, or are very poor in general. Gun control takes away a means to an end, it doesn't take away the mean.
And those low-rate countries (primarily European) have gun-control laws, which the narrator quietly glosses over.
Also, more diverse places tend to have higher murder rates, since it creates tensions between different ethnicities (could that be of an unspoken racial bias/xenophobia? Noo...). Texan cities tend to be quite homogenous, while Chicago is pretty diverse.
Gun control isn't the deciding trend in homicide, inequality is.
EDIT: I know that there are a bunch of other factors that also take part in this, reality is complex (so if someone comes with a simple solution or claims that a solution is simple, you should be wary...but I digress), but I believe that I coverd the most important things. Violence comes out of conflict, and inequality is a main source. I also never claimed that solving inequality in a healthy way is an easy thing to do.