Exactly, and that's the reason why you can use the Swastika as much as you want in Germany when the context makes clear that you're not using it for political purposes. These silly strawmen arguments do not help the discussion.
This mostly agrees with the text of the law, which appears to include a provision translating to "... shall not be applicable if the means of propaganda or the act serves to further civil enlightenment, to avert unconstitutional aims, to promote art or science, research or teaching, reporting about current historical events or similar purposes."
Reporting on the law suggests that the purpose is much stronger than simply avoiding its political use, but also to "avert social habitation". In particular, it appears that its use in, say, a video game would in fact be illegal, as Ubisoft assumed with its 2014 release "South Park: The Stick of Truth".
If I recall correctly, the Swastika is banned in Germany, even though it's a symbol with many meanings in many cultures. This means people can't express certain aspects of their cultures, visually, simply because the NSDAP chose to use the same logo. Context matters, you know.
Finally, I heard a law in Germany is about to get passed that is going to make large social networks program bots that automatically ban content based on whether it may contain hate speech or crime. Good satire will disappear from much of the German internet.