Didn't hear this radio feature, but the definition is not 100% correct, imho. Terrorist groups are defined in criminal law in § 129a StGB. This definition includes either
- conspiracy with the intention to commit crimes like murder, genocide, crimes against humanity or sth like that, without any further limitations, or
- conspiracy with the intention to commit crimes from a larger catalogue of felonies, incl. torching or use of explosive devices, but with some limitations concerning the reason for these crimes. This supposed ideological background doesn't cover only "actions against the state" though, but also actions with the intent to intimidate the people, which are suitable to damage the state as a whole.
I don't think, that this should be broadened. In fact, the law is widely criticized by civil liberties activists, because it was extensively used to persecute left-wing groups in the past. Even if they haven't done anything people would neccessarily classify as terrorism, just because investigations under 129a trigger a wide range of additional surveillance measures. Often, those investigation wouldn't end in a formal indictment, but just serve the purpose of gathering intelligence.
So, IANAL, but I don't think, that the Freital group isn't covered by anti-terrorism law at all. The NSU terrorists didn't directly attack the state either, but random immigrants, and nobody doubts them being classified as terrorists. Nonetheless, for many people it is kind of unusual, to bring charges like this, because the perpetrators didn't do much other right-wing criminals don't do as well. Their explosive devices weren't particularly sophisticated, their assaults didn't kill or badly hurt anybody, they didn't live undercover, etc.
The issue, if the Freital group are indeed terrorist, doesn't center around having them convicted for terrorism or "just" for multiple murder attempt and the other seperate charges, though, because it doesn't really matter for the degree of penalty. It is merely a question of authority. In German law, criminal investigations and the court system are almost exclusively under the supervision of the federal states. (A lesson learned from the Nazi era, not to concentrate too much executive power on central institutions.) To bring charges of terrorism is one of just a few cases, where the Federal Prosecutor General (Generalbundesanwalt) is authorized to take the lead in the investigations. In the past, he was very reluctant to do so, with the many attacks on refugee accommodations during the past couple of years.
That he did in this case is therefore widely seen as a sign of distrust to the local Saxon authorities to deal with it properly!
That's not unreasonable. In fact, many people in Germany already see Saxony as some kind of failed state, with police authorities and justice system deeply infected by far-rights. Weird decisions and priorities shown by Saxony prosecutors occur regularly, e.g. dropping of charges against right-wingers (or police officers accused of illegally cooperating with them) while persecuting left-wing people with ridiculous allegations. They even indicted the prime minister(!) of neighbor state Thuringia (from the Left party) for taking part in anti nazi protests in Dresden, Saxony's capital.
These so-called "citizen initiatives" were almost everywhere founded or at least dominated by members of far-right parties like NPD. Of course, there are places where a lot of people, who aren't necessarily fascists, got utilized by the organizers, but the connection between those "citizen initiatives" and militant right-wing extremists was real and obvious from the beginning, for everyone wanting to see it.