Knowing the local language, listening to the video and consulting other (German-language) sources reveal a little more:
A court hat ruled before that the protest in front of the embassy would be allowed to take place, but explicitly prohibited any recitation of or quotation from Böhmermann’s poem.
At the very point when Kramm violated that condition by going from pure literary analysis (which he seems to have a hard time reading because it contains so many big words) to explicitly quoting the poem, police step in.
They do so quite politely (“I’m sorry but…”) and Kramm of course plays it for effect. I couldn’t understand everything that was said in the video, but Kramm then continues in a load voice:
Kramm: “How about I continue to talk about this without my microphone?” (readying his notes).
Policeman: “Then I would have to take steps to prevent [that]”.
Kramm: "So if I now say that… " (at this point he reads from his notes again, apparently from the paragraph just before the direct quote).
This is the point when police take him away.
The immediate reason was to prevent the violation of the court-imposed conditions for that particular protest. They had no grounds to imprison him, I gather they just did the “usual”, which is to take him to a police station to formally take down & verify his name and address, and then let him go.
He’s being charged for violating the regulations concerning the public protest he organised (which might get him a fine), and he might theoretically be charged according to the same Lèse majesté paragraph as Böhnermann, seeing that he did essentially the same thing.
That, though, is a thing that the courts need to decide before anyone spends a single night in prison.