My analysis of this neglected story can be found at the Victorian Web, where it appeared some years ago: http://www.victorianweb.org/history/crimea/beck/1.html – or just do a search for “Mark Twain on the Crimean War” and the link should come right up.
I mention it because whoever wrote up the topic at Wikipedia evidently did not bother to read beyond the first page. Including the bibliography, there are in fact six pages. There you can also find reference to my article (not online) about teaching this story in Moldova.