BTW the guy who made those illustrations is Pekka Allan Manninen usually known as P.A. Manninen (I think that’s joke as PA in Finnish is short for perse auki (ass open) and means brokeass).
There are two main styles of English crossword puzzles: the one in the article and another type that is called a cryptic or British crossword which is little more sparse and has a different style of clue (each clue describes the word twice, but it’s up to the reader to decompose the clue into the relevant bits).