Hi Mark, that's a fair question. The counting and visual representation used in the video is more true to reality and how it sounds when you play it. Sheet music is, at best, a rough guide. It takes for granted that the reader knows how to interpret the rhythms given the "feel" of the song. If you'll notice at the top of almost every transcription in the book it says "swing" and then gives the eighth note interpretation as a triplet derivative.

Sheet music was not created with a swing eighth note in mind, so when using the interpretation of a swing rhythm, there is usually a little marking like this at the beginning of the piece so that the eighth notes don't need to be written as triplets (as that would be quite cumbersome).

Hope this helps? If you need more clarification let me know.

Short answer is: that's just how you write it, but the way I explain it in the video is how you play it.