The claim that hypertext is non-linear requires some correction. When hypertext authors and theorists say that the text is non-linear, they mean that the reader has a choice of paths through the text. These paths, generally marked by links, allow multiple ways of sequencing any particular reading. But of course, a reader can only ever choose one path at a time. So the text is linear, but not uni-linear. I prefer to call such texts multi-linear.
The ability for the reader to choose a path, however, is not merely a gimmick. The multiple paths mean that the hypertext author has to allow for reader choices. Consider the printed book; the reader has a choice of pages, but most begin with page one, and turn the pages in sequence. For narratives, this is the only way to read (leaving aside "Choose-Your-Own-Adventure" books). For poetry, individual poems will almost always be read line-by-line.
In hypertext, the choices make the meaning.