How is that kind of typesetting called in English?

I only found “runaround” in several dictionaries, but this sounds like it is limited to a subset of cases, where the text actually runs around another object. 

I don’t recall stumbling upon a specific term for this. But I think your example shows effectively two different techniques: 

1.  Using the text to form a specific shape, like in some forms of concrete poetry (works by Lewis Carroll comes to mind). I vaguely remember (or imagine?) an old thread on Typophile on the topic. If a proper term isn’t found, I think we could appropriate “topiary”. 
2.  Setting the type around non-rectangular shapes, for which “runaround” seems a good explanatory term.

I don't know if it's appropriate in this case, but I've come across the expression "Text wrap" or "Text wrapping" to describe this formatting of text, inside or outside objects.

By the way: in German we call it Formsatz (“shape typesetting”). I would be surprised if there is no English term, as there is a long history of this technique in letterpress. Doesn’t have to be as elaborate as in the image in the first post. It could just be a triangular ending of a paragraph and things like that.