Wiki syntax is a line-based syntax. There is /no/ wiki markup that spans lines. It makes editing much simpler: if you make a mistake and forget to close something, it gets closed off quickly. HTML is not designed to be human-editable; wiki syntax is.
I'm having a bit of trouble implementing the C parser because the Wikitext parser has a lot of quirks. For example, you say that no wiki markup spans lines, but if you take a look at: http://www.wikipedia.org/wiki/User:Marumari/Wikitext_Rendering_Quirks you can see that headers do span lines.