She refers to them as a gang to demonstrate to her students, almost all of whom are gang members or most likely future gang members, that gangs abuse power and that they do not improve a community. She knows that by introducing them in such a way, her students will be interested, and then as she starts to tell them of the atrocities that the Nazi "gang" committed against Anne Frank and her family, she hopes that her students will start to consider what their involvement in a gang might do to the innocent.
Similarly, after she builds up the Nazis as one of the most powerful gangs in history, she can demonstrate through Miep Gies (the woman who helped hide Anne and her family) that even someone who appears to be weak and insignificant can stand up against a huge gang.
Perhaps she was making the reference because in many ways the Nazis acted more like a gang than they did like a political party. If you look at the very forceful way in which they took power, their appeals to a very specific world-view, and the way they used power once they gained it, you could argue that they act a lot more like a neighborhood gang on steroids than a political party or political movement.
The other reason I think she was referring to them that way is it, in a way, belittles the Nazi Party, and is sort of a funny way of referring to them.