Of course, as many people know, that scene and in particular that seemingly clueless but extremely clever 19th century St. Petersburg detective inspired the Columbo series, which repeated this particular kind of "reveal dialogue" in basically every episode.
Christine's intention was that the reader would use the clues scattered throughout the book to work out who the culprit was. Indeed, like many other works from the Golden Age of Detective Fiction, the mystery is entirely solvable from those clues.
Christie ultimately added an epilogue to subsequent editions, which explains the mystery. In a sense, it's nice to have confirmation of what the solution is, but at the same time I like the idea that a mystery story doesn't necessarily need to include a solution.