Dude was German/Iranian, so that more or less rules out ISIS right there. It happened on the anniversary of Anders Breivik's attack, and the shooter claimed to be German and to hate foreigners. I bet Nazi, not jihadist.
On the one hand, we have a video of the guy shouting that he's a German and that he hates foreigners, and on the other we have an unconfirmed witness saying he shouted Allah Ackbar. Now, if he's a Nazi he obviously hates Muslims and would probably shout AA anyway because it would cause backlash against them. As for Iranian Nazis, Iran is literally the "Land of the Aryans" and they had incredibly close ties with Nazi Germany. So yeah, Iranian Nazi is way more likely than you...
Considering just how much Nazi Germany tried to convince the Iranians that they were kin, I don't think that's true. Some neo nazis undoubtedly hate them, but not all.