Of the 200 most popular names given to baby boys in 2012-2013, which have been named most often in the quizzes for American and British baby boys? You're not guessing the actual most common names, but what you think other people think American and British baby boys are called! In other words, you're guessing our collective stereotype of British and American names!
I think he means that, say, the most guessed name by quiz takers is 'Zorba'. Since this name doesn't make it in the Top 200, it is excluded from this quiz despite being the most guessed. So you're not showing the 'most guessed names' but the 'most guessed names among the ones that made it in the top 200' or something like that.
Good idea for a quiz, came out pretty well!